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.

(In reply to solution (if I understood correctly) by atheron)

Look at the first 6 numbers of your series:
1,24,2,25,3,26

The 2 is the mean of 1 and 3, 25 is the mean of 24 and 26.  You will certainly find others all the way throughout.  Yes, the solution was too easy :-(

Posted by brianjn on 2006-07-05 20:42:03