A Jumble of Numbers

Dec 06, 2004

A Jumble of Numbers

RAY: I'm going to start reciting to you the numbers between 1 and 100, including 1 and 100, perhaps.

I'm going to leave a space of 7 or 8 or 9 seconds between each one. So, the first number I'll give you is, say "2," then "3," then "27," then "51."

When I'm finished reciting all the numbers but one, I'm going to ask you which one I left out.

You can't use a pencil and paper. You can't write anything down. When I'm done I'll have given you not a hundred numbers, but ninety-nine.

Your job is to tell me which one I didn't give you. I'll give you a hint: There are two ways to do it. There's the easy way-- and there's the cowboy way.
TOM: Wouldn't I just add them up?

RAY: Well that's exactly what you would do. We learned as school kids that when you have a string of numbers and you want to find out what the sum of them is, you add the first number to the last number, which in this case is 100 plus one.

Multiply by the number of terms, which is a hundred, and divide by two.

You get 5050.

Keep a running total in your head. Let's say you came up with 5027.

The answer should be 23.

That's the cowboy way of solving this puzzler. But, there's an easier way.

Don't keep track of the hundreds digit or the thousands digit, just keep track of the first two digits.

When you're all done, instead of having a four digit number, you're going to have a two digit number.

TOM: So in the same example that you just gave, you're going to end up with the number 27.

RAY: Right. And you know that you need to have your last two digits be 50, so the answer is 23.

TOM: I still have to add things up because I have to remember the last two digits.

RAY: Right. Do we have a winner?

TOM: Our winner this week is Mike McNamara from San Francisco, California. And for having his answer selected at random from among all the correct answers that we got, Mike is going to get a $26 gift certificate to the Shameless Commerce Division at Cartalk.com.

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