Consider Erase the right 90
Find a sequence of the numbers from 1 to 100, not necessarily in that order, such that exactly ten groups of 10 form exactly ten distinct subsequences, which need not be continuous, in each of strictly increasing and strictly decreasing order.
List the 20 subsequences.
(In reply to
This should work by Jer)
It occurs to me that this is almost just a special case of p*q=r
which can have p+q increasing+decreasing subsequences.
If we want, say, a sequence of 15 numbers that have 3 groups of 5 we can go:
3 2 1 / 6 5 4 / 9 8 7 / 12 11 10 / 15 14 13
which has 3 increasing subsequences
3 6 9 12 15
2 5 8 11 14
1 4 7 10 13
and the obvious 5 decreasing ones.
If instead we order them
5 4 3 2 1 / 10 9 8 7 6 15 / 14 13 12 11
there are 5 increasing and 3 decreasing.

Posted by Jer
on 20160213 21:26:34 