Puzzler Answer: String Puzzler, Number A
RAY: You have in your possession two pieces of string. Let's say that each is a couple of feet long, but it doesn't really matter. And they can both be different lengths, it doesn't matter either. And they're burnable, like the fuses that they use to, you know, light dynamite. Now you could light either end of either string, and it would burn. In fact, if you lit one end of a string, it would burn in exactly an hour. Are you with me so far?
TOM: I've got it.
RAY: So, you light a string with what? The Zippo lighter. And it's lying on the table or on the floor.
TOM: -- It would burn right along and it would take one hour to be gone.
RAY: But here's the wrinkle: the strings do not burn at a constant rate. For example, the string might burn for two minutes and then go crazy and burn like mad and then slow down, and da-da-da. You don't know what rate the string's burning at any specific time. All you know is that in an hour's time, the whole string is burned. It's not linear. And not predictable.
TOM: Gotcha.
RAY: So, the question very simply is, with the Zippo lighter and these two strings, how would you measure 15 minutes of time?
TOM: Wow!
RAY: And I did mention, I think, that there are two answers to this. I'm only going to give you one answer this week.
TOM: Oh, you are?
RAY: Yes, because the other answer is, well, in the future.
TOM: Yeah!
RAY: So, you take String A, light both of its ends. You take String 2, and light one end. Well, what's going to happen? Because you lit both ends of the first string, in a half an hour's time, that string is going to burn up completely. A half an hour has gone by, and similarly, the other string you lit is going to burn for: half an hour's time. Right?
TOM: Yeah!
RAY: At which point, as soon as the first string has burned up completely, you'll light the remaining end of String 2, and because the first part of that string you lit is continuing to burn, it's going to take 15 minutes before those two flame fronts meet, and you'll have measured 15 minutes from the time that you lit the second string.
TOM: Exactly. So, the question could have been, how would you measure 45 minutes? Or 15 minutes, and it would be the same answer.
RAY: Exactly. Who's our winner this week?
TOM: The winner this week is Calvin Kuhnen from Columbus, Ohio.
[ Car Talk Puzzler ]
