Thursday, December 17, 2009

NPR Puzzle 12/13/09 An Answer of Numbers; A Number of Answers

Here's this week's puzzle:

It comes from Scott Kim, the puzzle maker for Discover Magazine.  He has a 2010 page-a-day calendar just out called Mind Benders and Brainteasers.  Here's one of the puzzles in it: Name five two-digit numbers that are evenly spaced out — like 32, 34, 36, 38 and 40 — in which all 10 digits from 0 to 9 are used once each.  What numbers are these?

Henry was here on Sunday and he worked out an answer almost immediately using jumps of 11:

50    61     72    83     94     (adding 11)

Then Ross read elsewhere that there are a total of four possible answers, so he wrote a computer program to find them all:

10     32     54    76    98     (adding 22)

18     36    54    72    90     (adding 18)

54     63     72    81    90     (adding 9)
You will notice a critical fact in this account of how these answers were deduced: I had nothing to do with them.   The only thing I provided was some off-hand comment about needing a number ending in zero.   I think I could have solved it with enough time, paper, pencils, and hair to pull out.  But luckily I didn't have to!   (I don't have the hair to spare...)

In other news, the cookies are all packed and most have been given away already.   I'm expecting a call from the Surgeon General to the effect that I'm an enemy combatant in the war against obesity.


Magdalen said...

By the way, and in my own defense, I programmed Blogger to post this at 3:06 this afternoon, which is says it did, but of course it didn't post until I manually told it to post.

Stupid Blogger.

Roxie said...

The first answer I came up with was the 9 sequence (took about 5 minutes). Then I read that people had found a total of four solutions, I thought about it, and decided that my answer was good enough :-) Too much math for one Sunday.