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 re(2): solution (with solution/spoiler) by Charlie)

Correction made to post re: solution (with solution/spoiler).

(Problem arose when ready to post I realized I had missed disks 45 through 47, I made only a quick check for the placement of these three disks and missed some obvious arithmetic means.Thank you for the comment, Charlie. I hope to be more thorough before posting in the future.)

Posted by Dej Mar on 2006-07-05 00:49:16