A set of 47 disks are consecutively numbered 1 to 47 and placed in a row as follows: 1, 2, 3, 4, ... 45, 46, 47.

Rearrange the disks so for any two given disks A and B, the disk equal to their arithmetic mean doesn't lie between them. For example, Disk 4 cannot lie between Disk 1 and Disk 7 since the arithmetic mean of 1 and 7 is 4. However, since 7 is not equal to the arithmetic mean of 1 and 4, Disk 7 may lie between Disk 1 and Disk 4.

it was pretty easy to see that the disks could be placed correctly by placing odds and evens in right spots. I started with 1,gap,2,gap,3... all the way to 24 and then filling those gaps starting from the beginning with 25 and so on...

The order was like this:

1,24,2,25,3,26,4,27,5...21,44,22,45,23,46,24,47

Correct me if there's something wrong.. The solution felt so easy that I thought I understood something wrong..

Posted by atheron on 2006-07-05 13:57:46