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View Full Version : A prime number puzzle to get you thinking

clop
2006-Jun-03, 07:45 AM

To solve this puzzle you must fill in the grid below using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Each digit must appear once in the grid.

http://i48.photobucket.com/albums/f208/tumkin/prime.jpg

The 4-digit number B must be a multiple of the 4-digit number A.

Four of the five 2-digit vertical numbers must be prime.

Good luck!

clop

Tumkin Technology

clop
2006-Jun-04, 09:43 PM
Too difficult for you all eh?

clop

antoniseb
2006-Jun-04, 09:51 PM
I started giving it some thought but got distracted. I think it wouldn't be *that* difficult. I was looking at it and figured that the last digit of A must be 5 and the last digit of B must be 0. This means that the non-prime two-digit number of in the right-most slot. It also limits the penultimate number in B to either 3 or 9. Also, the numbers on the bottom row would all have to be odd, meaning that most of the numbers on the top have to be even. This gave me a pretty limited list of primes to be working from, and only a few ways to collect them to meet the use-every-digit constraint.

That's as far as I got before a baseball game got really interesting and then I lost the puzzle on my task list.

ToSeek
2006-Jun-04, 10:54 PM

Besides 0, the other digits in the bottom row are 1,3,7, and 9. (There are no two-digit primes ending in 5.)

The first digit of A must be a 2 or a 4. (If it were any larger, then any multiple would be more than four digits.)

The first digit of B has to be a 9. (1, 3, or 7 wouldn't work.)

I took a couple of educated guesses after this and quickly got the answer.

montebianco
2006-Jun-09, 02:01 AM
Unless I've done something appallingly silly, the solution is unique.

ToSeek
2006-Jun-09, 03:33 AM
I only came up with one possible answer.

clop
2006-Jun-09, 07:08 AM
Unless I've done something appallingly silly, the solution is unique.

It is a unique solution. Rather neat really.

clop

ToSeek
2006-Jun-09, 03:29 PM
It was pretty cool.