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Did You Solve this STEM Mindbender?
March 21, 2010


Here was the cool puzzle that CMU’s Women@SCS, sent for you to solve.  Below it, we’ve published the answers that you all sent in.


There is an island with miniature natives on it. Once a year, an Evil Giant visits the island. The Evil Giant has the natives line up, all facing the front of the line, and places either a red or a blue hat on each native’s head. Starting at the back of the line, each native tries to guess the color of her hat.

Now, remember, every native can hear what the other natives say. So, when a native says the color of her hat, all the other natives can hear too.

If the native guesses right, she gets to stay on the island with her friends. If she is wrong, the Evil Giant takes her away from the island and away from her friends.

How can the natives design a strategy — before the Evil Giant begins placing the colored hats on them — to keep as many of their friends on the island as possible?

How many natives can stay on the island?

Here are the Answers that iTwixie Girls Sent In:

avatar I guess: all of them?

avatar Have the back person say to the person in front th e color of that person’s hat?

avatar Have the last native say the color of the first persons hat and pass it on to
the first person. Only the last person will get kicked off.

Here is the Answer:

Only the native that answers first cannot be saved for sure — it’s a 50:50 chance. Here’s why: She looks at the hats in front of her. If there is an even number of red hats, she says “red”, otherwise, he says “blue”. So, she says the right color with 50:50 chance.

The next one counts the number of red hats. If there is an even number of reds and the previous one said “red”, she concludes he must be blue, if there is an even number of reds and the previous one said “blue”, she concludes he must be red, if there is an odd number of reds and the previous one said red, she must be red and if there is an odd number of reds and the previous one said blue, she must be blue.

This way of thinking is called an algorithm. It goes on for all the natives. They count how many reds there are in front of them (odd or even) and take into account what the previous natives have said to get their color right. Thus, every native can be saved with 100% probability, apart from the last native (the native who answers first) who can be saved with 50%, or half, probability.

Cool, right?

So it looks like Eyeheartart12 solved it! Congratulations, Eyeheartart12! Send in your parent’s home address to info@iTwixie.com and we’ll send you a cool t-shirt!

Check in next week for iTwixie’s STEM (science, technology, engineering and math) puzzles from our friends at CMU’s Women@SCS!

Thank you, CMU’s Women@SCS for this cool puzzle! You really got us thinking!

{pub}Login (or join and then login) and come back to this page to send in your answers to the puzzle!{/pub}

{reg}Remember, none of your answers will show up until March 20, 2010, when we announce the solution to this puzzle! Good luck!{/reg}

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