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: solution (with solution/spoiler) by Dej Mar)

The following sets appear within Dej Mar's list of numbers, in the order shown, and have the mean lying between the two end numbers:

 45  33  21
 45  25  5
 45  41  37
 45  37  29
 47  35  23
 47  27  7
 47  43  39
 47  39  31
 46  34  22
 46  26  6
 46  42  38
 46  38  30

Posted by Charlie on 2006-07-04 22:00:56