Given a clock, rearrange six consecutive numbers on its face, so the sum of every pair of adjacent numbers is a prime.

Sorry ahead of time for the lengthy explanation!

The solution I got was that the clock would read: (Starting from the top, going in a clockwise direction) 12, 1, 2, 3, 4, 9, 10, 7, 6, 5, 8, 11.

First I noticed that the numbers that are being rearranged must be consecutive. That means that the other six consecutive numbers must already be in such a way that the sum of the pairs of adjacent numbers are prime. The only six consecutive numbers that fit the criteria were 11-4. That meant they must remain in their usual place on the clock.

I next tried to find what would be next to the 4. The only unused numbers that would fit were 7 and 9. Then I tried to see which numbers would work with the 7 and 9. The unused numbers that worked with 7 were 10 and 6. The numbers that worked with 9 were 10 and 8. Since 10 would fit in the 6 o'clock location no matter which number was there, I placed it there.

I used the same process with the position next to the 11. 8 and 6 worked with 11, and the only number that worked with both 8 and 6 was 5. So, I placed the 5 in the 9 o'clock location.

This left me with a clock reading: 12, 1, 2, 3, 4, _, 10, _, _, 5, _, 11.

I decided to place the 9 between the 4 and the 10. I placed the 8 between the 5 and the 11. I then put the 7 and 6 into place. I checked all the sums, and they worked.

Posted by Emma on 2004-08-06 20:56:02