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 20060704 22:00:56 