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Gray Watson Thoughts 2002.10.24
Your Brain Teasers Suck

[ Just found this interesting mail that I got last year and I thought it was amusing so I'll post it. This is the exception from the general mail I get about my teasers, but it is not the only one of its kind for sure. ]

From: SC <scprincess@...>
Date: Thu, 24 Oct 2002 16:08:10 -0400 (EDT)
Remote-Host: ns25.statefarm.com
Subject: Brain Teasers

Your brain teasers suck. First of all, the way you programmed your page does not allow for any answer, including the correct answer, to be typed in; it still says it cannot read it correctly.

Secondly, the answers for the "Lets Make A Deal" question make no sense. Why would you want to change from the initial curtain picked? Also, why, after the 1st curtain is open and there are only 2 left that could contain cars behind them, are the chances of a car being behind the chosen curtain 75%? It would be 50% because you cannot choose from a curtain that is already open.

As for the 3 Hats, your question is: "If the ball is black, what are the chances of you reaching back into the same hat and finding that the remaining ball in the hat is black?" If the ball is black then chances that the remaining ball is black is 50% because you have either chosen the hat with the black & white ball, or the hat with the 2 black balls. You could not have possibly chosen the hat with the white balls. If there is either the white ball or the black ball left in the hat you have a 50% chance of choosing another black ball.

I believe you should think about the things you put on your website, it really reflects a lot about the author.

Well okay then. Thanks for the comments. Here's my response.

To: scprincess4@...
Subject: Re: Brain Teasers
From: Gray Watson

Your brain teasers suck.

K.

First of all, the way you programmed your page does not allow for any answer, including the correct answer, to be typed in; it still says it cannot read it correctly.

This is a legitimate gripe. I'll take a look at your answers and see what went wrong. If you have specific examples, I'd appreciate it. [ See below ]

Secondly, the answers for the "Lets Make A Deal" question make no sense. Why would you want to change from the initial curtain picked? Also, why, after the 1st curtain is open and there are only 2 left that could contain cars behind them, are the chances of a car being behind the chosen curtain 75%? It would be 50% because you cannot choose from a curtain that is already open.

It is 66% (2/3) not 75%.

As I mention in the description, you choose 1 curtain out of 3. What are your chances of getting it right? 1/3. What are the chances that it is in either of the other 2 curtains? 2/3. This _never_ changes. The fact that Monty opens and shows you an _empty_ curtain, only confuses the question. It doesn't change the odds. If he opened a _random_ curtain then it would be different. You aren't making the choice _after_ he opens the empty curtain.

How about if there were 100 curtains and you choose 1 and Monty shows you 98 empty curtains?

If the ball is black then chances that the remaining ball is black is 50% because you have either chosen the hat with the black & white ball, or the hat with the 2 black balls. You could not have possibly chosen the hat with the white balls. If there is either the white ball or the black ball left in the hat you have a 50% chance of choosing another black ball.

But the trick is that if you get a black ball, you are more likely to have chosen the hat with the 2 black balls. Twice as likely.

I believe you should think about the things you put on your website, it really reflects a lot about the author.

Sigh. I've _thought_ about this a lot. The answers are correct. Yours is a standard reaction from someone who just doesn't get it. Do some web searches or talk to math and statistics people you respect before you disregard the answers. Here's some links for you to read about the Monty Hall problem:

http://www.cut-the-knot.org/hall.shtml

Oh and here's my new description page with a C test simulation:

http://256.com/gray/teasers/lets_deal.html

BTW, I didn't get either of these problems when I was given them. But then again I _understood_ the answers when there were explained to me and I wasn't rude.

I then went back and look at my web logs at SC's guesses to check my pattern matching code. Looks like the pattern matching worked fine.

Question SC's Guess Correct Answer
Let's Make a Deal #1 no yes
Let's Make a Deal #1 yes or no yes
Let's Make a Deal #2 50% 33% or 1/3
Three Hats 50% 66% or 2/3
Three Hats 75% 66% or 2/3
Three Hats "75%" 66% or 2/3
Number of 7s 21 20

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