Hats Off

“Colonel Mustard killed Mr. Body in the billiard room with the candlestick”–began no mystery novel ever. The entire genre is called “whodunit” because the joy of reading is trying to figure out–or in my case waiting to be told–who did what to whom and why. The whole point of a mystery novel is the “aha!” toward the end. So that’s the reason! Of course! I should have known!

It’s great to be fooled. It’s great to figure it out. The delight of a good novel is the rollicking ride. There’s nothing better than a good MacGuffin–the detours the protagonist takes on the road to the solution. There’s nothing more pleasurable than a sparkling red herring. Remember in “Bedazzled” when the devil–superbly portrayed by Peter Cook–commits brazenly nasty acts? He scratches records; he gives parking tickets; but the worst thing that he does is rip out the last page of mystery novels. Can you imagine? Not knowing the ending is the worst thing ever.

If there is anything more exquisite than the culmination of all the clues and uncertainty at the end of a good mystery novel, what about a virtuous logic problem? Not a stupid, junior high question where the aliens swoop in as the answer to the kidnapping. And certainly not a problem with a trivial answer. There’s not much joy in solving x + 3 = 5. No, what I love is a problem that I have to think about for several minutes–hours is even better–before the answer comes to me like a smack on the back of the head.

Here are two of my favorites, one with which you are likely familiar, one which may give gratify your sense of wonder and accomplishment. You may wish to allow a few minute for the “fox, chicken, grain,” problem. The “five hats” problem could take longer–a lot longer.

First Problem: A child needs to take three possessions–a fox, a chicken, and a bag of grain–across a river. There is only room in the canoe for the child to carry one of the three items at a time. The issue is that the child cannot leave the fox with the chicken; foxes eat chickens. Nor can the child leave the chicken with the grain; chickens eat grain. How can the child get all three-fox, chicken, and grain-across the river?

Second Problem: Three men are seated in a room, two are blindfolded, one is blind. A woman addresses the three men as follows: “I have five hats; three are black, two are white. I am going to place one hat on each of your heads and discard the other two.” She does exactly what she said she would–places one hat on each man’s head and throws away the other two hats. She then removes the blindfold from the first man and says, “Can you tell me what color hat is on your head?” The first man looks at the hats on the heads of the other two men, thinks for a moment, and replies, “no, I cannot.”

She removes the blindfold from the second man and says, “Can you tell me what color hat is on your head?” The second man looks at the hats of the heads of the other two men, thinks for a long time, and replies, “no, I cannot.”

The woman addresses the third man who is blind. “Can you tell me what color hat is on your head?” The blind man replies, “yes, I can.”

What color is the hat on the blind man’s head? How does he know?

I hope you enjoy these problems. Needless to say, I won’t give you the answers. Although I will gladly answer a question and supply a hint or two. But now as always, let’s direct our attention to parenting: If the joy is in discovery, why do we as parents, give our children the answers to problems that they would be better served to solve on their own? The fundamental purpose of having a crumby job at 17, for example, is to learn that you don’t want to have that same crumby job at 27. Being told, “you won’t like getting up at oh dark hundred and being yelled at by an idiot boss” is nothing compared to actually getting up at oh dark hundred and being yelled at by an idiot boss.

Last example for the holiday season: Here’s a 500-piece puzzle. I have taken the liberty of unwrapping and assembling it before giving it to you. Bad gift. The whole POINT of a puzzle is the joy of putting it together. That’s why puzzles are sold in the box in lots of pieces. Otherwise “puzzles” would be called “posters” or “placemats.” And no one would buy them. Children LOVE putting puzzles together. Nobody likes being handed the solution.

Every valid, meaningful lesson is internalized from experience. Let’s allow our beloved children to learn, to enjoy learning, and to have as many “aha!” moments as possible! The alternative is to allow the fox to eat the chicken, the blind man not to know what color hat is on his head, and for the actual murderer of Mr. Body to go unpunished.