Hummings of a Happy Hurkle

This is a hat problem. The participants are supposed to be infinitely clever Mensa members, each wearing a hat bearing a number, such that they can see each other’s numbers but not their own. The hat numbers are integers, greater than zero. There are 3 participants (A, B and C, or Albert, Brian and Clarence if you prefer), and the number on one of the hats is the sum of the numbers on the other two. They take turns as follows:

A: I don’t know my number.

B: I don’t know my number.

C: I don’t know my number.

A: My number is 25.

What are the numbers on the other two hats?

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Here are two puzzles, superficially similar, but different answers.

A. Alf meets Bert, and asks him how many children he has, and of what sex.
The puzzle: if Bert has two children and at least one of them is a boy, what are the odds that he actually has two boys?

B. Alf now asks the same questions of several more people, until he gets to Charlie.
The puzzle: if Charlie has two children and at least one of them is a boy, what are the odds that he actually has two boys?

C. Alf goes back to Bert, and asks him what days any boys were born on.
The puzzle: if Bert has two children and at least one of them is a boy born on a Tuesday, what are the odds that he actually has two boys?

D. Alf now asks the same questions of several more people, until he gets to Dave.
The puzzle: if Dave has two children and at least one of them is a boy born on a Tuesday, what are the odds that he actually has two boys?

This strange puzzle and/or variants of it was originally set by Martin Gardner. The surprising thing is that the exact same question can have two different answers depending on the assumed context from which the odds should be calculated. There are enough clues here to make the answers fairly obvious.

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Anyone fancy a logic puzzle/game? I just ran across this one.

http://www.tomjubert.com/irrational

It’s a download, text-based propositional logic with a cute back story. Only 10 questions, but it certainly made me think.

Enjoy!

Multiple Choice Question:
If you choose an answer to this question at random, what is the chance you will be correct?
A: 25%
B: 50%
C: 0%
D: 25%

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It’s rare to read a negative book review from the scientific community written with this kind of candour and certainty. Stephen Wolfram of course is the author of Mathematica and a pretty bright lad. Seems he went astray somewhere, or at least this reviewer thinks so.

The book is “A New Kind of Science”.

The reviewer calls it “A Rare Blend of Monster Raving Egomania and Utter Batshit Insanity.”

http://www.cscs.umich.edu/~crshalizi/reviews/wolfram/

Worth a read, even if you have no interest in the book, science, Wolfram…

• Flustrated
• Misunderestimated
• Heathengelical
• Spontanimosity
• Exorberant
• Traumajesty
• Overflowded
• Ambiviolence
• Craptcular
• Fugly
• Manscaping
• Misconscrewed
• Malamanteau

These are all malamanteaus. Anyone need that explained? Anyone know any others?

For those desperate enough: http://en.wikipedia.org/wiki/Talk:Malamanteau#original_text_and_creation_information.

Sometimes, I feel just like this…

(the little girl, that is.)
Sorry, unknown attribution.

http://thisisindexed.com/wp-content/uploads/2010/05/card2564.jpg

Two witnesses provided evidence in court.

Tom is a somewhat reliable witness giving accurate testimony 70% of the time. Harry is less reliable, giving accurate testimony 60% of the time.

Both testified to the same effect.

What is the chance that their evidence was indeed accurate ?

Think carefully now.

[Thanks to Mark W for this one.]

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