# It’s Follow-Up Friday: Hats Off to You edition!

Welcome to Follow-Up Friday!

By this time, you know the drill. Follow-Up Friday is a chance for us to revisit the subjects of previous posts and bring the PuzzleNation audience up to speed on all things puzzly.

And today, I’d like to revisit the subject of brain teasers.

A few years ago, we posted a riddle that had been making the rounds online. It centered around four men buried up to their necks in the ground, each one trying to figure out what color hat he is wearing.

It’s a great exercise in logic and deduction, one that most solvers unraveled after a few minutes.

As it turns out, there’s a more complex version of this riddle. But this one involves 100 people!

One hundred prisoners are lined up single file, facing in the same direction. Each prisoner will be randomly assigned either a red hat or a blue hat.

No one can see the color of his own hat. However, each person is able to see the color of the hat worn by every person in front of him. So the person at the head of the line cannot see the color of anyone’s hat, the second prisoner can see only the first prisoner’s hat, the third can see the first two prisoners’ hats, and so on. The last person in line — the 100th prisoner — can see the colors of the hats on all 99 people in front of him.

Beginning with the last person in line, and then moving to the 99th person, the 98th, etc., each will be asked to name the color of his own hat. If the color is correctly named, the person lives; if incorrectly named, the person is shot dead on the spot.

Everyone in line is able to hear every response as well as hear the gunshot; also, everyone in line is able to remember all that needs to be remembered and is able to compute all that needs to be computed.

Before being lined up and given their hats, the 100 prisoners are allowed to discuss strategy, with an eye toward developing a plan that will allow as many of them as possible to name the correct color of his or her own hat (and thus survive). They know all of the preceding information in this problem. Once lined up, each person is allowed only to say “Red” or “Blue” when his turn arrives, beginning with the last person in line.

What would your plan be to save as many people as possible? How many prisoners can you definitely save?

It’s an absolutely diabolical riddle, one that definitely taxed my puzzle skills. And different plans have different chances for success! Will you save half? 75%? Can you save everyone?

[Click here and scroll down for the solution, courtesy of the folks at IO9.]

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# Beware the Brain Melter…

I’m a huge fan of brain teasers. I love pitting my mind and mental quickness against word puzzles and other challenges, so brain teasers are perfect.

A terrific example of a quality brain teaser appeared here a while back: the Men in Hats problem (pictured above).

It’s a great brain teaser because it’s deceptively simple, but requires careful, outside-the-box thinking to figure out how to solve the puzzle.

But there’s another kind of brain teaser out there that’s not intended to be solved. These are more tricks or bits of wordy gamesmanship than brain teasers. I like to think of them as brain melters.

Here’s an example of a brain melter I tweeted a month or two ago:

True or false? Thare are five mistukes im this centence.

Now, parsing it out, you can see the misspelled “thare” (1), the misspelled “mistukes” (2), the misspelled “im” (3), and the misspelled “centence” (4).

But the statement says there are five mistakes when there are only four, which would make the statement false. If you count “five” as a mistake, then it becomes five mistakes, which makes the statement true. But if five mistakes is true, then saying “five” ISN’T a mistake, so the total goes back to four mistakes, and…

You see? You soon find yourself in a brain-melting loop that never goes anywhere. It’s like the barber who shaves only the townsmen who don’t shave themselves. So does he shave himself? If he does, he doesn’t. If he doesn’t, he does.

Still with me?

Okay, here’s another brain melter. (The one, in fact, that inspired this blog post.)

If you choose an answer to this question at random, what is the chance you will be correct?

A) 25%
B) 50%
C) 60%
D) 25%

At first glance, this seems simple. There are four options, so the chances of being correct should be 1 in 4, or 25%.

But wait. Two of the answers are “25%”, meaning that A AND D could lead to the right answer, so those odds become “50%”.

But “50%” as an answer only appears once, so the chances of choosing “50%” are only 25%.

And if you keep following that chain of thought, you circle around and around and around, going from 50% to 25% and back again while your brain dribbles out your ears and down into your shoes.

Beware the brain melters masquerading as brain teasers, my friends.

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