Thursday, February 27, 2014

Einstein Puzzle Non-Spoiler Answer Checker

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I built this little checker in order for those who don't want the answer spoiled for them, to check their work. This is specifically for the Einstein Puzzle.

Click here to go back to the puzzle

Click here to go to the walkthrough

How to use it:

Let's say you want to check to see if the "Brit lives in the Red house". Below are a few charts separated by the Nationality of the owner. I've hidden the answers by changing the background color to the same as the font color. You can see inside the boxes if you highlight them.

Here are more detailed instructions:

Step 1. Go down to the section with the heading "Brit".
Step 2.Next, look at the chart. Find the column that says "color", and find "Red" in there.
Step 3. You should see something that looks like a little grey rectangle, like this:
Red Y
Highlight the black square with your mouse (left click and hold it down. Then drag over it). It should look something like this:

Red Y

Step 4. 
Key: 
  • If the letter inside the grey rectangle is "Y", that means that (in our example), the Brit DOES live in the red house. 
  • If the letter inside is a "N", then the Brit does not.

Step 5. Go ahead and check your answers. Careful not to highlight too much and spoil it for yourself though!

Note: You may have a few issues if you are using a mobile.
------------------------------------------

Brit

Drinks Pet Smokes Color Number
Tea N Dogs N Pall Mall Y Red Y N
Coffee N Birds Y Dunhill N Green N N
Milk Y Fish N Blends N Yellow N Y
Juice N Cats N Bluemaster N Blue N N
Water N Horses N Prince N White N N
---------------------------

Swede

DrinksPetSmokesColorNumber
Tea NDogs YPall Mall NRed NN
Coffee NBirds NDunhill NGreen NN
Milk NFish NBlends NYellow NN
Juice YCats NBluemaster YBlue NN
Water NHorses NPrince NWhite YY

-------------------------------

Dane

DrinksPetSmokesColorNumber
Tea YDogs NPall Mall NRed NN
Coffee NBirds NDunhill NGreen NY
Milk NFish NBlends YYellow NN
Juice NCats NBluemaster NBlue YN
Water NHorses YPrince NWhite NN

--------------------------------

Norwegian

DrinksPetSmokesColorNumber
Tea NDogs NPall Mall NRed NY
Coffee NBirds NDunhill YGreen NN
Milk NFish NBlends NYellow YN
Juice NCats YBluemaster NBlue NN
Water YHorses NPrince NWhite NN

-----------------------------

German

DrinksPetSmokesColorNumber
Tea NDogs NPall Mall NRed NN
Coffee YBirds NDunhill NGreen YN
Milk NFish YBlends NYellow NN
Juice NCats NBluemaster NBlue N4 Y
Water NHorses NPrince YWhite NN

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Einstein's Puzzle Thorough Walkthrough (Spoilers)- Pt3

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This is the walkthrough for Einstein's Puzzle. If you haven't read the original puzzle/question, you should go ahead and click on the link below. Below will be the explanation of the method I utilized to solve the puzzle. If you want to avoid spoilers you should view the original question before reading below.

For Previous parts: Part 1, Part 2

You can find the Puzzle here.

Click here for a Spoiler-free answer check

Walkthrough:

So this is simple logic puzzle with no real tricks or second guesses. So all you really need is organization to solve this puzzle. I'll be breaking this walkthrough into parts, so you can try it on your own after reading an article:

Here's how I solved it.


-----------------------------------------------------
So here is my three categories of clues (for your ease of reference)

          Direct Link:
  1. Brit * Red House
  2. Swede * Dogs
  3. Dane * Tea
  4. Green * Coffee
  5. Pall Mall * Birds
  6. Yellow * Dunhill
  7. #3 * Milk
  8. Norwegian * #1
  9. Bluemaster * Juice
  10. German * Prince

    Unlinked:
  11. Green (L) White
  12. Blends (N) Cats
  13. Horse (N) Dunhill
  14. Norwegian (N) Blue
  15. Blends (N) Water

    Negative Link:
  16. Green ~ White
  17. Blends ~ Cats
  18. Horse ~ Dunhill
  19. Norwegian ~ Blue
  20. Blends ~ Water
Key:
*  = linked
(L) = is left of
(N) = is next to
~ = Is not linked to

The reason I do this is to make referencing and understanding the clues much faster and more efficient. I refer to each of these clues by #. For instance the link between house #3 and Milk is Clue 7.
----------------------------------------------------

So this is probably the point where most people become frustrated and begin to guess. But we don't want to do that. 

Instead, you start to look at the clues more carefully and see how they interact with one another.


Deduction 1:
So we know that the Norwegian is house #1 (Clue 8), and is on the far left. We also know that the house next to it is Blue (Clue 14). Since there is only 1 house next to it, then house #2 must be blue. So Blue * #2. We can use that to update our lists. 

If it can't be blue, then it can't be #2. And vice-versa.
Sadly this only really affects the Brit, by eliminating the possibility that he could be #2.

Deduction 2:
We know that the Green house is to the Left of the white one. So if Green is #3, then White must be #4. or if Green is #4 then Green is #5. We get some interesting results from this:

  • If we combine this with Deduction 1, which says that #2 is blue, then it means that either Green is #3 and white is #4, or Green is #4 and white is #5. Essentially, Green can't be linked with #5, nor #1.
     
  • Since we know White has to be to the left of Green, then Green can't be linked to #1, since white would have to be #2, which clashes with our knowledge that Blue is #2. Additionally, White can't be #1 since there would be no way for Green to be on the left (there is no house #0). So neither Green nor White can be #1, nor #2.
The Norwegian's data is updated. Since he is #1, It eliminates the possibility of him being Green and White. Since the Brit is Red, and house # 2 is blue, this means that we know the Norwegian is in Yellow. 

This updates the Data of almost everyone. 
Since the Brit is in Red, and the Norwegian is in Yellow
  • Swede: Green, White, Blue
  • Dane: White, Blue
  • German: Green, White, Blue
Additionally, Since we know the Norwegian is in Yellow, Thanks to Clue 6, we also knows he smokes Dunhill.

More updates to possibilities:
  • Brit- Pall Mall, Blends, Bluemaster
  • Swede- Blends, Bluemaster
  • Dane- Pall Mall, Blends
  • Norwegian- Dunhill
From Clue 13, we know the Dunhill Smoker is next to the Horses, and as a result is not a Horse owner (clue 18). Additionally, since the Norwegian is #1 (clue 8), and since he is the Dunhill smoker, then #2 is the Horse owner (Clue 13). So if you don't have the possibility to own horses, you can't be #2
  • Norwegian- Birds, Fish, Cat
  • Swede- Dogs
    • (Can't be #2)
      • #3, #4, #5 are the remaining possibilities
  • Brit- Birds, Fish, Cat, Horses
  • Dane- Birds, Fish, Cat, Horses
  • German- Fish, Cat, Horses
-------------------------------
At this point, you start to double check the non-nationality link clues against your newly acquired information (The ones that link non-nationality traits together): 

(small)Deduction 3:
Since we know house #1 * yellow, #2 * Blue, then all we have left are Red, Green, and White. Since we know that Green must be to the left of White (clue 11), then Red can only be #3 or #5 since it can't be in the center.
  • So the Brit is limited to #3, or #5.

(small)Deduction 4:
Due to Clue 5- only the person who smokes Pall Mall can be the bird owner, and vice versa.
  • Update: Norwegian can only own: Fish Cat, Horses
(small)Deduction 5:
Clue 9 says that Bluemaster and Juice must be linked. So only if both of those are possibilities can it apply to you.
  • Update: Norwegian can only drink: Coffee, Water
Deduction 6:

It almost appears as if we hit a wall. However, we know that the Norwegian can only drink either Coffee or Water, which is a 50/50 shot. We have the opportunity to do a hypothetical with good results.

(water possibility)
Since we know that the Blends Smoker lives next to the Water drinker (Clue 15), I figure it would be more interesting to start with this hypothetical. So if the Norwegian of #1 was the water drinker, then #2 * Blue *Blends.Of the remaining nationalities, there is only the Dane who fits that category. 

This would mean:
  • Dane * #2 *Blue *Blends
    • Also ~Cats (clue 17), and (N) Cats (clue 12)
  • (as a result) Swede would be the Bluemaster Smoker
    • And juice drinker (clue 9)
  • (as a result of that)
    • Brit- Drinks: Milk (result)
      • Smokes Pall Mall (result)
    • German- Drinks: Coffee
Here's how my chart looks:
Made a mistake. Swede shouldn't have Yellow on there. My bad.

We might then look back at our clues and look for new links given all the information we received:
  • Clue 5 says the Pall Mall smoker owns the birds:
    • The Brit owns the birds
  • Clue 4 says the person in the green house drinks coffee
    • The German drinks coffee and is in the green house
      • As a result he cannot be house #5 since the white house must be to to his right.
      • Thus the Swede is in the White house

  • Clue 13 says the Horse owner lives next to the Dunhill smoker.
    • The Norwegian smokes Dunhill and lives at #1, which means our friend the Dane at #2 owns the Horses.
  • Clue 7 says #3 is a milk drinker. Thus, the Brit who drinks milk is in house #3.
    • Brit * #3
This also means that the German is at house #4, and the Swede is at #5. We have all the houses all set up. All that remains is the fish and cat.


  • Clue 12 says that the Blends smoker is next to the Cat owner. Since the Dane is the Blends smoker, and lives in #2, either #1 or #3, must own a cat
    • Since the Brit owns a bird, then that only leaves the Norwegian with the Cat.
    • The German would be the fish owner.

Answer: The German owns the fish.

Double check your answers by seeing if it fits with every one of the clues. 
-----------------------------------------

Well that's it for the walkthrough of the Einstein Puzzle. I hope you enjoyed it and learned something along the way!

Read more →

Wednesday, February 26, 2014

Einstein's Puzzle Thorough Walkthrough (Spoilers)- Pt2

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This is the walkthrough for Einstein's Puzzle. If you haven't read the original puzzle/question, you should go ahead and click on the link below. Below will be the explanation of the method I utilized to solve the puzzle. If you want to avoid spoilers you should view the original question before reading below.

For Previous parts: Part 1

You can find the Puzzle here.

Skip to here if you just want a spoiler free answer check

Walkthrough:

So this is simple logic puzzle with no real tricks or second guesses. So all you really need is organization to solve this puzzle. I'll be breaking this walkthrough into parts, so you can try it on your own after reading an article:

Here's how I solved it.

A visual depiction of linking.

-----------------------------------------------------
So here is my three categories of clues (for your ease of reference)

          Direct Link:
  1. Brit * Red House
  2. Swede * Dogs
  3. Dane * Tea
  4. Green * Coffee
  5. Pall Mall * Birds
  6. Yellow * Dunhill
  7. #3 * Milk
  8. Norwegian * #1
  9. Bluemaster * Juice
  10. German * Prince

    Unlinked:
  11. Green (L) White
  12. Blends (N) Cats
  13. Horse (N) Dunhill
  14. Norwegian (N) Blue
  15. Blends (N) Water

    Negative Link:
  16. Green ~ White
  17. Blends ~ Cats
  18. Horse ~ Dunhill
  19. Norwegian ~ Blue
  20. Blends ~ Water
Key:
*  = linked
(L) = is left of
(N) = is next to
~ = Is not linked to

The reason I do this is to make referencing and understanding the clues much faster and more efficient. I refer to each of these clues by #. For instance the link between house #3 and Milk is Clue 7.
----------------------------------------------------

So here's when I finally get to the step that you probably jumped to on your first attempt of this problem. The filling out of the chart. I start by filling in the Direct clues:



Which doesn't provide us too much for a very specific reason: Our grid here makes it quite difficult to enter information for links between things that are not tied down by nationality. Where do you put the clue about how "Green * Coffee"? 

So this is where a lot of organized thoughts stop, and people start to flail. But not us! We shall keep this grid, and try to solve it. How? By working with what we can learn about each Nationality!

-------------------------
I will demonstrate the method I utilized and my thought process with a simple 4 step process:

Step 1: Lets start with the Brit. What do we know about him? 
  • Brit
    • Red House (Clue 1)
Step 2: Hmm, that doesn't help us much. But then we remember that all things that are linked to the other Nationalities are not linked to the Brit. So we get:
  • Brit
    • Red House
    • ~Tea (Clue 3)
    • ~Dogs (Clue 2)
    • ~#1 (Clue 8)
    • ~Prince (Clue 10)
Step 3: Ok, so that tells us a bit more, but what else can we find out about the Brit? Well, since he is linked to the red house, then only things linked to "Red House" will affect him. Everything that effects houses of other colors are not attributed to the Brit.

  • Brit
    • Red House
    • ~Tea
    • ~Dogs
    • ~#1
    • ~Prince
    • ~ Coffee (Clue 4)
    • ~ Dunhill (Clue 6)
Step 4: Ok, is that absolutely ALL I can get from it? Well, there are those "Unlinked clues". Maybe I can add those in:
  • Brit
    • Red House
    • ~Tea
    • ~ Coffee
    • ~Dogs
    • ~Prince
    • ~ Dunhill
    • ~#1
    • ~(L) White
    • ~(N) Norwegian

I repeat this process with each person of Nationality:
  • Swede
    • Dogs (Clue 2)
    • ~Red (Clue 1)
    • ~Tea (Clue 3)
    • ~Prince (Clue 10)
    • ~Pall Mall (Clue 5)
    • ~#1 (Clue 8)
    • ~(N) Blends (Clue 12)
    • ~(N) Dunhill (Clue 14)
  • Dane
    • Tea (Clue 3)
    • ~Red (Clue 1)
    • ~Green (Clue 4)
    • ~Dogs (Clue 2)
    • ~#1 (Clue 8)
    • ~#3 (Clue 7)
    • ~Prince (Clue 10)
    • ~Bluemaster (Clue 9)
    • ~(N) Blends (Clue 15)
  • Norwegian
    • #1 (Clue 8)
    • (N) Blue (Clue 14)
    • ~Blue (Clue 19)
    • ~Red (Clue 1)
    • ~Dogs (Clue 2)
    • ~Prince (Clue 10)
    • ~Tea (Clue 3)
    • ~Milk (Clue 7)
  • German
    • Prince (Clue 10)
    • ~#1 (Clue 8)
    • ~Red (Clue 1)
    • ~Yellow (Clue 6)
    • ~Tea (Clue 3)
    • ~Juice (Clue 9)
    • ~Birds (Clue 5)
    • ~Dogs (Clue 2)
    • ~(N) Cats (Clue 12)
    • ~(N) Horses (Clue 13)
------------------------------
Whew, that took a while. But now its time to do the fun part with the analysis. It's a good time to refresh our memory about Sherlock Holmes' famous line about deduction:

"How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?"
     The Sign of the Four, ch. 6 (1890)

So how does this phrase pertain? Well, with each of our gentlemen above, we have eliminated the impossible. So what remains? Does it provide us with any solid facts?

No? Well lets look at what remains for each in each category:
  • Brit-
    • Drinks- Milk, Water, Juice
    • Pets- Cats, Horses, Birds, Fish
    • Smokes- Pall Mall, Blends, Bluemaster
    • House Color- Red
    • House Number- #2, #3, #4, #5
  • Swede-
    • Drinks- Coffee, Milk, Juice, Water
    • Pets- Dogs
    • Smokes- Dunhill, Blends, Bluemaster
    • House Color- Green, Yellow, Blue, White
    • House Number- #2, #3, #4, #5
  • Dane-  
    • Drinks- Tea
    • Pets-Birds, Fish, Cat, Horses
    • Smokes- Pall Mall, Dunhill, Blends
    • House Color-  Yellow, Blue, White
    • House Number- #2, #4, #5
  • Norwegian-
    • Drinks- Coffee, Juice, Water
    • Pets-Birds, Fish, Cat, Horses
    • Smokes- Pall Mall, Dunhill, Blends, Bluemaster
    • House Color- Green, Yellow, White
    • House Number- #1
  • German-
    • Drinks- Coffee, Milk, Water
    • Pets-Fish, Cat, Horse
    • Smokes- Prince
    • House Color- Blue, White, Green
    • House Number- #2, #3, #4, #5
--------------------------------------

Here's your chance to go and try to solve it for yourself. If you're eager to see how it is solved, continue onto part 3

Or double check your answer (spoiler-free) here
Read more →

Tuesday, February 25, 2014

Einstein's Puzzle Thorough Walkthrough (Spoilers)- Pt1

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This is the walkthrough for Einstein's Puzzle. If you haven't read the original puzzle/question, you should go ahead and click on the link below. Below will be the explanation of the method I utilized to solve the puzzle. If you want to avoid spoilers you should view the original question before reading below.

You can find the Puzzle here.

Skip here if you want a spoiler-free answer check

Walkthrough:

So this is simple logic puzzle with no real tricks or second guesses. So all you really need is organization to solve this puzzle. I'll be breaking this walkthrough into parts, so you can try it on your own after reading an article:

Here's how I solved it.
All the possible pets.

------------------------
Here is the question, for reference:
  1. The Brit lives in the red house
  2. The Swede keeps dogs as pets
  3. The Dane drinks tea
  4. The green house is on the immediate left of the white house as you stare at the front of the 5 houses
  5. The green house owner drinks coffee
  6. The person who smokes Pall Mall raises birds
  7. The owner of the yellow house smokes Dunhill
  8. The man who lives in the house in the center drinks milk
  9. The Norwegian lives in the first house
  10. The man who smokes Blends lives next to the one who keeps cats
  11. The man who keeps horses lives next to the one who smokes Dunhill
  12. The owner who smokes Bluemaster drinks juice
  13. The German smokes Prince
  14. The Norwegian lives next to the blue house
  15. The man who smokes Blend has a neighbor who drinks water
Main Question: Who owns the fish?
----------------------------------------

Listing the Possibilities

What I did first was make a list of things we needed to keep track of, as well as all the possibilities within each group (they are all mentioned in the clues):

  • Nationalities: 
    • Brit 
    • Swede 
    • Norwegian
    • Dane
    • German
  • Drinks: 
    • Tea 
    • Milk 
    • Water 
    • Juice 
    • Coffee
  • Pet: 
    • Dogs
    • Birds 
    • Fish 
    • Cat
    • Horses
  • Smokes: 
    • Pall Mall 
    • Dunhill 
    • Blends 
    • Bluemaster 
    • Prince
  • House Color: 
    • Red 
    • Green
    • Yellow 
    • Blue 
    • White
  • House Number: 
    • #1 
    • #2 
    • #3 
    • #4 
    • #5
This list will be important for deduction. 

--------------------------------
Categorizing the Clues
Once I finished making a list of all possible choices, I began to arrange the clues into groups depending on the type of information they gave. 

I noticed there were a few types of clues:
  1. The first type would give a direct "link" between two components. For instance, the first clue says "The Brit lives in the Red House". Since everything is unique (only one house color per one person, and no duplicates, and same for the rest of the categories), we understand that "Brit" and "Red House" are linked. And that anything that happens to Red house will happen to the Brit.
  2. The second type of clue gives "Unlinked clues" that deal with house positioning. For instance, the tenth clue says that the Blends smoker lives next to the Cat Owner. We can't immediately link any two components together, but we can utilize this when we have more information about house placement.
    • The third type of clue comes from the second type of clue. Again, if we look at the tenth clue, we see that the Blends smoker lives next to the cat owner; as such, we note that the Blends smoker can't be the cat owner.
So here is my three categories of clues:

          Direct Link:
  1. Brit * Red House
  2. Swede * Dogs
  3. Dane * Tea
  4. Green * Coffee
  5. Pall Mall * Birds
  6. Yellow * Dunhill
  7. #3 * Milk
  8. Norwegian * #1
  9. Bluemaster * Juice
  10. German * Prince

    Unlinked:
  11. Green (L) White
  12. Blends (N) Cats
  13. Horse (N) Dunhill
  14. Norwegian (N) Blue
  15. Blends (N) Water

    Negative Link:
  16. Green ~ White
  17. Blends ~ Cats
  18. Horse ~ Dunhill
  19. Norwegian ~ Blue
  20. Blends ~ Water
Key:
*  = linked
(L) = is left of
(N) = is next to
~ = Is not linked to

The reason I do this is to make referencing and understanding the clues much faster and more efficient. I refer to each of these clues by #. For instance the link between house #3 and Milk is Clue 7.
----------------------------------------------------

Here's your chance to go and try to solve it for yourself. However, If you're eager to see how it is solved, continue onto part 2!

Or double-check (spoiler-free), here
Read more →

Monday, February 24, 2014

Try the Einstein Puzzle

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I love logic puzzles. They are fantastic for practice with deductive reasoning, but to be honest I was never very efficient with the way that I solved them. So when I recently heard about the "Einstein Puzzle", I decided I would try my luck at making an organized method for solving them. But before I get into that, I thought I would give you a chance to solve it for yourself.

Supposedly, the rumor goes that when Einstein created the problem, he believed that only 2% of the population would be capable of solving it. And while the validity of that statement is dubious at best, it is a puzzle that can cause issues if you aren't careful.

The Einstein Problem is just a simple logic puzzle. There are five people of different nationalities, who all love a specific drink, smoke, pet, and house color. No two people in this group of five have the same drink, smoke, pet, or house color. 


Here are the clues:
  1. The Brit lives in the red house
  2. The Swede keeps dogs as pets
  3. The Dane drinks tea
  4. The green house is on the immediate left of the white house as you stare at the front of the 5 houses
  5. The green house owner drinks coffee
  6. The person who smokes Pall Mall raises birds
  7. The owner of the yellow house smokes Dunhill
  8. The man who lives in the house in the center drinks milk
  9. The Norwegian lives in the first house
  10. The man who smokes Blends lives next to the one who keeps cats
  11. The man who keeps horses lives next to the one who smokes Dunhill
  12. The owner who smokes Bluemaster drinks juice
  13. The German smokes Prince
  14. The Norwegian lives next to the blue house
  15. The man who smokes Blend has a neighbor who drinks water

The main question is: Who owns the fish?
----------------------------------------
If you want to double check your answer without it being spoiled, try the spoiler-free answer checker

That's all it is. Try your luck, if you get stuck or just want to see the method I used to solve it. Click here for the walkthrough.

I believe you can find the original source here.
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Learning about the Mind through studying Mnemonics (Part 2)

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This is the second part of an article, I highly suggest you read the first part before continuing with this segment. You can find the article here.
In part 1, we were introduced to the idea that our brains are much like a little attic, and have limited capacity to remember things. Only by grouping and packaging ideas together into clusters, were we able to hold a large amount of things in our mind at one time.
So basically, the concept of "clustering" a core component to our ability to think about more complex topics and ideas. It allows us to hold more things in our short-term memory at one point in time.
Clustering is also not limited to numbers, in fact it is probably most prevalent within words and ideas. For instance, take this sentence:
"I tipped the waitress at my restaurant."
While it differs from culture to culture, this is basically a completely intelligible sentence to most people. The thing is, the amount of things you have to understand in order to comprehend this sentence is far exceeding the limits of our short-term memory.
Let's take the simple idea of "restaurant" for instance. For many of you, its pretty clear and obvious right? You might say: "A restaurant is a place you go, where you pay people to cook and provide you with food."
It is so commonplace that we don't realize that we have to understand several things before being able to grasp the idea of a "restaurant":
  1. The idea of eating
  2. The idea of food
  3. The idea of money
  4. The idea of a place to go
  5. The concept of payment
  6. The idea of cooking.
  7. etc

The idea of a "restaurant" is a cluster of many ideas and thoughts, and yet we can use it and refer to it without overburdening our minds. We can also pull the list of ideas from it without much effort.
Also, this goes without mentioning "waitress" and "tipping", which are also clusters in themselves.
So we know that we obviously use clusters on a daily basis and have them. But how are they made?
----------------------------------------
The Making of Idea Clusters
Let's demonstrate the formation of a cluster through conscious means by using a mnemonic.
Let's say we had a list of items that we had to memorize:
  1. Banana
  2. Trumpet
  3. Shoes
  4. Confuscious
  5. Beer
  6. Optimus Prime
  7. Bicycles
  8. Television
  9. Socks
  10. Raccoon
Take a look at this list of words. I want you to look at it, and then recite the contents of the list in the right order back to me (from memory obviously). Go ahead and try it before coming back here:
Having some trouble? It shouldn't be too surprising as every item in that list appears to be completely unrelated to every other item on that list.
But never fear, even the clusters of "Kitchens", "Football", "Star Wars" and "Space" were a collection of seemingly unrelated items to us at one point. Over time, we were able to formulate connections between all those unrelated items into a single cluster.
Despite the fact that all these concepts are essentially completely random and unrelated, we should still be able to unite and cluster them together into a single unit. We just need the glue to do so, which brings us to:
The Linking Method
The Linking Method is a mnemonic people use to memorize lists of things and their order. It uses visual imagination and absurd imagery to create memorable links between items in the list.
I first heard about the Linking method in an audiobook by Derren Brown, a famous magician/mentalist. The idea he presented was simple: link the objects together one after another as if they were links in a chain; As we keep pulling on the chain, each item will remind us of the next item, which will remind of the next one after that.
Allow me to demonstrate. We will start with the first two items on our list:
1.Banana2. Trumpet
I connect these two items together by imaging something bizarre or absurd involving the two:
I picture a banana, and imagine peeling it back. But instead of seeing the inner fruit of a banana, I instead see a trumpet.
The image is so crazy and strange that I can't help but remember it. With that, I would have connected two links. The next step would be to link the second link with the third:
2.Trumpet
3.Shoes
Again, I imagine an absurd image that involves the two items:
After the trumpet is peeled from the banana peel, I zoom in on the trumpet buttons, and imagine them fitted with crazy slippers, high heels, and tennis shoes.
This crazy and yet memorable image would help me connect the second and the third items together. I would continue this process for the third and fourth, and then the fourth and fifth, and continue likewise until I finished with the list.
Note: I personally try to imagine one item leaving hints to the next item, or even morphing and becoming another. You should try out a few methods and see what works best for you.
My disgusting Amalgamation
After I finish the list, I would begin with the first item of the list and think back on the absurd image I created. The banana would then remind me of trumpet, which would remind me of shoes, which would remind me of Confuscious, and so on.
  • Banana-> Trumpet
  • Trumpet-> Shoes
  • Shoes->Confuscious
  • etc
In the end, you would have created a sort of imaginary filmroll, with which we could come up with things like "beer", "optimus prime", and "socks" from the imaginary image of a "banana".
Go ahead and try to remember the list again. You should be better equipped for the task now.
We've in essence, created a sort of artificial cluster. Now if I mention "The list", you're very likely to be able to rattle off the contents such as "Confuscious", or "Optimus prime".
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What Does this Mean?
So what have we learned from all this? Well, we should have begun to understand that it is through the clustering of ideas that we are able to hold more complex thoughts and ideas in our head, which help us understand more complex topics.
Additionally, we've learned how to make artificial clusters through the linking method and imagery.
One thing to note, however, is that the linking method works for a reason: absurd and bizarre imagery appeals to our minds and is very well retained. Mnemonics only work because they take advantage of the way our minds are naturally organized. The Linking method utilizes the fact that our minds put a great importance on retaining memories that are strange and absurd.
A mnemonic known as the Method of Loci, or Memory Mansion, was utilized by the Ancient Greeks, and will be the topic for the next part.
Until then.
If you're interested in Derren Brown and his Mnemonics Podcasts, click here for his wiki, and here for his website.
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Sunday, February 23, 2014

Take the Simple 3 Question Challenge: The CRT

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Here are 3 questions that I would like to pose to you. Go ahead and try answering them.

The first question:
A baseball bat and a baseball together cost $1.10. The baseball bat costs $1.00 more than the baseball. How much does the baseball cost?
The second question:
It takes 5 toy-makers 5 minutes to make 5 toys. How long would it take for 100 toy-makers to make 100 toys?
The third question:
There's a special patch of lily pads in a pond. The size of the patch doubles every day. On the 48th day, the patch has covered the whole pond. How many days did it take for the patch to cover half of the pond?
As you can see, the questions are quite simple for the most part. However it would be a mistake to conflate simple with easy. The test was given at world renown universities such as Harvard, Princeton, and MIT with results that may surprise you.
  • At Harvard, the average score was 1.47 correct answers with 57% getting a score of 0 or 1
  • At Princeton, the average score was 1.63 correct answers with 45% getting a score of 0 or 1
  • At MIT, the average was a bit higher at 2.18 correct answers with 23% getting a score of 0 or 1
But what does this mean?
I should tell you that the test you've just taken is known as the CRT, or Cognitive Reflection Test. It was a test formulated by Shane Frederick, a professor at MIT. It was used as an intelligence test, and tested how people responded to various biases.
Personally, I only heard about it through a book called "Mastermind" by Maria Konnikova (fantastic read if you ever get a chance). The version I wrote above is a bit different from the one given in the book, but the spirit is there.
Now then, onto the answers:
The answers are (SPOILERS):
  1. The ball costs $0.05
  2. It takes 5 minutes
  3. 47 days
If you are like the general populace, its likely that you got at least one of these questions wrong. But why? What does it mean for the way we think?
Here are the incorrect answers that are frequently given:
  1. $0.10
  2. 100 minutes
  3. 24 days
Now is time to look into why we might make those mistakes:
1. Why would someone think $0.10 is the answer? Well, just think about the numbers: the bat and the ball are $1.10 right? The bat costs $1.00 more than the ball. If we have that, then we might think that doing $1.10 - $1.00 would get the price of our ball of $0.10. If all we think about is the strict numbers, it makes perfect sense that we would get $0.10 as the answer.
2. This is sort of a matter of pattern recognition being used in the wrong way. We notice the pattern of 5, 5, 5: which is 3 of the same numbers in a row. With the new set up we have 100, 100, ___. We recognize that both seem to set up for a sequence of three of the same number, and are inclined to finish the sequence with a 100. Again, this is a matter of looking at the numbers without looking at the context.
3.The last one is the lily pond that is covered with lily pods in 48 days. We hear that the patch doubles in size every day, but seem to forget it quite quickly, or are inclined to push it aside. Instead we focus on the numbers of 48 days, and the key word of HALF. With some simple math we find that half of 48 days is 24 days. And thus we end up with our answer.
So what does this say about our intuitive and innate thinking?
Well essentially we are very good at ignoring context, but very good at pulling numbers out and recognizing patterns. The key reason why so many people were mistaken in their responses is because they would take the key numbers out of the problem, and try to figure out how to solve it like a simple math problem. Also that people don't naturally double check, as double checking or reading closely would probably have fixed many of the mistakes that were made.
However, it should be noted that people might do better if they think it is a riddle. They will read more carefully and look for pitfalls that could confuse them.
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Friday, February 21, 2014

Riddle # 1 Walkthrough-The Liar and Honest Village (Spoilers)

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This post is meant to walk you through the thinking you would have to do in order to solve the Liar and Honest Village riddle. If you have not read the riddle question yet, you should click here.

Warning, reading below may spoil the answer. 


Here's some food for thought(Hint)
Notice that the liar guard's answer will always be the opposite of the honest guard's answer. Given that, so long as their answers differ, you won't be able to get anywhere in this riddle.
But that's the kicker.
So long as their answer differ.
So how do you get it that the guard will answer the same thing, no matter what village he is from?
There's your hint, if you don't want the answer, stop reading, you've been warned.
Answer(spoilers- no pictures to avoid spoiling, sorry!)
So you have to get the guard to answer the same thing no matter what village he is from. But how do you do that? Well, it might be easier to phrase the question differently:
  • If he's from Honest village, how would you get him to answer like he's from Liar village?
  • If he's from Liar village, how would you get him to answer like he's from Honest village?
Well, if he's from Honest Village, he would tell the truth. So if we ask him something like, "If you were from liar's village, what direction would you say the Honest Village is?". He would then answer like hes a liar, and tell you the direction to Liar Village. The other way is Honest Village.
If he's from Liar Village, he would say the opposite(lie). So if we asked him something like, "If you were from Honest village, what direction would you say the Honest Village is?". Well, he's from Liar Village, so he wouldn't give the Honest man's answer, he would give the opposite and lead you to Liar Village. The other way is Honest Village.
You might think, oh that's it! Except it isn't. You have to be able to combine these questions into one. This is how the first question of "If you were from Liar Village, what direction would you say Honest Village is" would look like this:
  • If honest- He would give the direction to liar village
  • If liar- He would give the direction to honest village
Which is no help. The same goes for the second question. Simply having them postulate if they were from a particular village is no help. They have to imagine being from the OPPOSITE village.
So the question would be something along the lines of: "If you were from the village across from yours, what direction would you say Honest village is?"

Answer
The result is this:
  • The Honest guard pretends to be a liar- Gives Liar village's whereabouts
  • The Liar guard pretends to be honest village citizen, but gives opposite response- Gives Liar village's whereabouts
And that's that. One of the classic riddles broken down. I hope this helps some people!
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Practice Lateral Thinking with Riddle # 1:The Liar and Honest Village (The Question)

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Riddles are fantastic ways to practice lateral thinking!

If you've heard riddles, you've probably heard the one about the liar's village and honest village. But allow me to remind you anyways:
Somewhere there lies a pair of villages. The first village is called "Honest Village" where all of its inhabitants always tell the truth. The second village is called "Liar Village" where all its inhabitants always tell lies.
One day, you are walking towards the village and run into a fork in the road. One road leads to the Honest Village, while the other leads to the Liar Village, but you are unsure which road leads to which village.
However, there is a guard at the fork- who is willing to answer 1 question. You are uncertain which village he is from, but wish to know the location of each village.
What do you ask?
I realize there are a multitude of variations of this puzzle, and you have probably heard them before. But I decided to go with a rather bare bones version with a single guard (I believe the first version I heard had two guards).
Anyways, rather than jumping straight in and thinking of a multitude of questions, we should probably observe the possibilities.
  • The guard could be from the Honest Village, or from the Liar Village
  • The Liar Village could be on the right, or it could be on the left
  • The Honest Village could be on the left, or on the right
  • The two villages can't be in the same direction
So lets just think of a rather commonly asked question:
"Which way to Honest Village?"
Suppose the answer was: Honest Village on the right, Liar Village on the left. Here's how it would look:
  • If the guard was a liar, he would say "Left"
  • If the guard was honest, he would say "Right"
This isn't a useful response for the person who wants to go to Honest Village. Since you are unsure whether the guard is from Liar village or from Honest village, you won't be able to say for certain which direction lies Honest Village.
That's all the hints I can give you without starting to walk you through to the answer. If you really are stumped, perhaps you can start reading the walkthrough.

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Learning about the Mind through studying Mnemonics (Part 1)

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Mnemonics and the Brain Attic


"I consider that a man's brain originally is like a little empty attic..." said Sherlock Holmes, "... It is a mistake to think that the little room has elastic walls and can distend to any extent."
It was back in the late 1800s that Sherlock Holmes first described the brain as a sort of attic with limited space. He described it as so small and limited that information, such as knowledge of the solar system, would clutter the room and would have to be thrown out.
Despite how dramatic the fictional Sherlock Holmes was in his insistence that his brain attic was constantly in danger of being cluttered, his vision of the mind was actually somewhat true.
A groundbreaking article by George A. Miller found that our short-term memory was able to retain approximately Seven plus or minus two clusters of information.

Really? Just 5-9 pieces of information? It seems quite odd when we think about it. After all, average people are able to easily list off over 10 movie titles, 10 book titles, and all their favorite foods without breaking a sweat. Average people can even recall 10 digit phone numbers or recite the alphabet. While memory geniuses are capable of memorizing decks of cards and entire plays quickly and without great effort.

So if our brains are really that limited? How is it that we are capable of remembering so much?

Well, one of the main reasons is because of Mnemonics. While typically the term refers to "memory aids" or "memory techniques" that are used by people to memorize large loads of information. I find that the techniques work simply because they mimic the way the brain naturally processes information.

So lets talk a little about mnemonics, and how they mimic the way our minds naturally organize and process information.
I'm going to be referring to a couple sources, the first is "Mastermind" by Maria Konnikova, the second is George A. Miller's famous piece on short term memory, and the last is from my compiled knowledge of Mnemonics and the method of Loci.
Let's get right to it
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The first thing we can note is that our memories tend to be rather limited. There have been recorded cases of people with a seemingly infinite "photographic memory", but for the large majority, our memories tend to have a breaking point.
For instance, lets say we have a series of numbers: 1, 8, 9, 4, 6, 3, 7, 5, 2, 2, 1,6
I want you to read it like this:  one, eight, nine, four, six, three, seven, five, two, two, one, six, and try to remember and recite it back.
You will most likely fail somewhere between the fifth and ninth digit. As if you had run out of space to place it.
This was essentially what was found in George Armitage Miller's article, "The Magical Number Seven, Plus or Minus Two". Basically through several tests, Miller discovered that our ability to retain information in our short term memory was limited to seven plus or minus 2 spaces. So in a sense, there is a limit in how much capacity our memory has, sort of like an attic with only minimal space.
So how is it that we are able to easily remember 10 digit phone numbers when we couldn't even recall 10 numbers? Well, it is because our mind often uses a mnemonic technique without our knowledge.
There is a caveat to the Miller study. Miller notes that our short-term memory doesn't store things in their component parts, but rather in clusters. Allow me to explain with an example.
Remember our number list up there? Why don't you take every two numbers, and group them into a single unit: 1,8 will become 18; 9, 4 will become 94, and so on. Go ahead and read them as: "eighteen, ninty-four, etc"
What you'll notice is that you're probably able to remember about 5-9 pairs.
So why is that interesting? Well, we might think of 18 as something made of two different components: a "1", and a "8". But our brain doesn't think of it like that. Especially if we say it as "eighteen". This is even the case with "ninty-four", which we think of as a mix of "ninty" and "four".
This is not limited to just numbers, we have plenty of "clusters" of information all around us.:The concept of "kitchen" is packed to the brim with pots, pans, knives, food, refrigerators, and the such that are easily unpacked; the same goes for sports like "soccer", and other activities.
It's as if our brain said, "You can put seven plus or minus two things into the brain attic". But each of those things could be a large box or backpack filled to the brim with other small items. The key is knowing how to unpack it.
This would be a perfect time to introduce more artificial mnemonics. Take a look at this:
ROYGBIV
I'm guessing that if you have a background in art or have taken an art class you have probably come across it at one point or another. This is a mnemonic cluster for remembering the colors (and their order) of the rainbow.
R-Red
O- Orange
Y-Yellow
G-Green
B-Blue
I-Indigo
V-Violet
This is what I meant about "being able to unpack the bag". In order to utilize this mnemonic, you have to know
  1. The cluster itself
  2. What it pertains to (colors of the rainbow)
  3. The colors of the Rainbow
Without those components you will be hard pressed to decipher the mnemonic. As far as I know, ROYGBIV means nothing in the field of biology, or in a football match. Additionally, if you don't know anything about the colors of the rainbow (don't know their names), it will be hard for you to unpack it. All you will know is that there is a color that starts with R, one that starts with O, etc.
So this part should have been a clear demonstration of mnemonics, and given a taste of how our brain utilizes them. Next time, we'll continue talking about mnemonics, and how clusters can be formed with words.
Click here for Part 2!
If you're interested in George A. Miller's article. Here is a link to the Wiki pageIf you're interested in Mastermind by Maria Konnikova (I recommend it), look here
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Tuesday, February 18, 2014

Learn about Context and the Deductive Process

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Imagine this:

You are waiting in a hospital waiting room, just looking through the magazines and observing the other patients as they wait to be seen by the doctor. When a man who had just entered tripped and fell over the leg of one of the chairs. He stands up and begins to gesture and yell loudly at the receptionist.

Assume this is all you know. What can you tell about the man? Well, your first inclination might be to try and look at the thing that makes him stand out: his gestures and yelling. Perhaps we assume that his actions are a result of anger, and that he has a nasty temper and is one who tries to blame others for his pain and suffering. In short:
He has an Outburst -> He has a nasty temper
But can we really?
It's a principle mistake to simply isolate a particular instance or action and assume that its indicative of all actions and inclinations that the person has. To deduce a person's thoughts and actions, one must be willing to be flexible and mold their deductions around all of a person's actions rather than just boxing them in with general frames.

The goal is to be as accurate with your deductions as possible,
 not to just to put people into a general category.
So what can we do? How can we make our deductions more accurate and more flexible? The answer lies in creating another layer or filter. You can't just think outburst -> temper. You have to consider Context.
Still not fully following? Let's use the same story we had earlier, but change the context.

New Context:On the alternate universe Htrae, the standard method of conversation is through wild gesturing and yelling. Any other method is considered rude. Whispering is used in angry fits.
 As you can see, if our original story had taken place on alternate universe Htrae, rather than Earth, our deduction of Outburst-> Nasty Temper would hold no weight at all.
From this, we see that context matters greatly in determining what actions have meaning, and which do not. Additionally we see that our deductions have to be keen to the context of the scenarios.
But lets return to Earth and see what the context might be able to tell us about the man.
Granted, the outburst may be telling of a nasty temper, but that is only one interpretation. The context may tell us more: The man is in a hospital, he is entering the waiting room of a hospital, he trips over the leg of a chair, he yells at the receptionist and only at the receptionist. He is also there at that time, as well as date.
What does this tell us? To understand it, we must break it down into parts:

Add caption

  1. He is in a hospital. Who goes to a hospital? Everyone? Well, WHEN do people go to hospitals? Well, either they work there, are visiting, or are sick. The vast majority of the people who visit, are sick. And given the whole of his actions, it seems plausible that the man could be sick.
  2. He is entering the waiting room. Not only that, but he is headed to the receptionist and not straight into the entrance of the door. So he is probably likely to be going to talk to the receptionist.
  3. He trips over the leg of a chair. Is he clumsy? Is there something wrong with his leg? Was he distracted by something? And if so, by what?
  4. Why does he yell at the receptionist? Is it because of his inclination to blame his pain on others? Why just the receptionist and not the other people there?
As you can see, the actual process of deduction using context is not as simple as the fixed deduction that we are inclined to use. However, we can learn a great deal more by formulating these questions, and then answering them by observing his actions.
The process of deduction requires a great deal of preparation, observation, and flexibility. Luckily it is also something we get better at through practice and time. As far as contexts go, it also can work well with many people within the same contexts- e.g. The hospital set applies to everyone in the waiting room, including you.
With a bit of practice and a little bit of work, understanding the context can go a long way.
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