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Optimal Order (Posted on 2016-02-10) Difficulty: 4 of 5

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.

No Solution Yet Submitted by broll    
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re: This should work | Comment 2 of 5 |
(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 2016-02-13 21:26:34

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