CarTalk Puzzler

[albionmoonlight]

My coworker and I have rolled this over in our heads for a couple of days to no avail. Anyone here able to figure it out?


http://www.cartalk.com/content/puzzler/transcripts/200449/index.html

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.

[Barkeep49]

Well if you know this is happening, I would add up all the the numbers between 1 and 100 (which excell tells me is 5050) and then after each number you give me I would subtract it. Whichever number is left is the missing number.

[KWhit]

That's what I came up with too.

I'm glad I didn't scroll down to see your answer, Barkeep. That was fun to try to think of an answer to. I got confused because at first I thought they were looking for the answer to be the number that is left and I kept saying to myself - that's impossible to figure out given the information! Then I realized they were looking for the technique used to get the answer.

BTW, I love Car Talk.

[QuikSand]

I'm presuming that just adding each number to a running total is the "hard" way to do this. It's not much of a puzzle if that's the answer.

I'm guessing they are looking for something a little more novel.

[QuikSand]

...but the (very deliberately inserted) space of 8 or 9 seconds does sound like it might be designed just for that purpose - to allow a reasonable person to adjust his running sum. Possible, I suppose.

[digamma]

I'm presuming that just adding each number to a running total is the "hard" way to do this. It's not much of a puzzle if that's the answer.

I'm guessing they are looking for something a little more novel.
I was thinking the "cowboy way" might be the angle for the more novel approach, but I'm stumped there.

[albionmoonlight]

dola--

they have been on a bit of a mini-roll. I really liked the one that they did last week with the pills.

[albionmoonlight]

Well, whether it is the "hard" way or not, it was better than anything I came up with (nothing). I'll take it.

[QuikSand]

Thinking outside the box a bit...

From 00 to 99, we ought to see every digit represented a total of 20 times, right? Ten times as the first digit, and ten times as the second digit.

Maybe there's some sort of method that you could use to represent how many times each digit has been used, using your fingers -- move them up then down or each time you see the appropriate digit. If they all started up, they should all finsih up, except the two digits that were not usd their final time.

That leaves me unable to break a tie between 37 and 73, though.

...dunno...

[KWhit]

Cowboy Way:

After each number is recited, you pull out that many pubic hairs and make small stacks of them on the table in fornt of you. Once all the numbers have all been recited, you count the number of hairs in each pile and sort them from 1-100.

Locate the missing pile and there's your answer.

Don't ask me why it's important that pubic hairs be used. That's what makes it the Cowboy way.

[DanGarion]

It didn't say I couldn't use a calculator :D