A set of 47 counters is consecutively numbered from 1 to 47 and placed in a row as follows: 1, 2, 3, 4, ... 45, 46, 47.
Rearrange the counters so that, for any two given counters A and B, the counter equal to their arithmetic mean doesn't lie between them.
For example, Counter 4 cannot lie between Counter 1 and Counter 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, Counter 7 may lie between Counter 1 and Counter 4.