Puzzler of the week

[Scott MacLean]

This week's puzzler:

The other day in the shop I had two Toyota Camrys each side by side. One of them didn't run. It cranked and you turn the key and wa, wa, wa, but it wouldn't fire up. And the other one was in for an emissions test. So I tell Ralph to do these two cars. So he takes the emissions tester probe. He sticks it in the tail pipe of the car, which he is supposed to do the emissions test on. He opens the hood. The next thing I know he is cranking this car, wa, wa, wa. It won't start.

He then takes the probe out of the tailpipe, sticks it in the other car. He gets into the car that wouldn't start. And he turns the key and of course, it doesn't start. It does the same thing that the first car did. Wa, wa, wa. I say to him, "What the hell are you doing?"

I assumed at first that he went to the wrong car. He then explains to me what he is doing. I say ah ha! What's he doing?

Last week's puzzler:

Once upon a time there lived a king who wished to find the wisest man in the realm to be his assistant. He summons the three wisest men to his court and he administers the following test:

He sits them in a circle, facing each other and he says "I'm going to put either a red hat or a white hat on each of your heads."

He proceeds to place a red hat on each of their heads.

Obviously, they can see each other, but there are no mirrors in the room so they can't see what's on their heads. He says "If you can see a red hat, raise your hand." They all raise their hands. Then he says, "If you can tell what color hat you have on, stand up."

They all look at each other. Nobody moves. Finally, one guy stands up.

He announced, "I'm wearing a red hat."

How did he know?

Last week's puzzler answer:

The clue is that for a moment or two, nobody moved. Nobody knew for certain what color his hat was, and that's what told the wisest guy that all of the hats were red. Here's how he figured it out. Each of them had acknowledged seeing at least one red hat. Now, Wiseguy #1 knows he can see two red hats, right? Now, *if* Wiseguy #1 had a white hat on, Wiseguys #2 and #3 would have known what color their hats were.

Step 1:
Wiseguy #1 knows he can see two red hats.

Step 2:
Wiseguy #1 thinks, "Hey, if I were wearing a white hat, Wiseguy #2 would see one red hat and one white."

Step 3:
Wiseguy #1 then thinks, "If I were wearing a white hat, and Wiseguy #2 saw one red hat and one white (and if he were wearing a white hat himself), then Wiseguy #3 would have seen two white hats. So, Wiseguy #3 wouldn't have raised his hand to the first question.

Finally, it hits him. Wiseguy #1 thinks, "If that were true, Wiseguy #2 would be sure that he had a red hat. But since Wiseguy #2 was actually unsure about his hat color, it can only mean one thing, my hat is red."