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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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Solution This should work | Comment 1 of 5
Consider scaling 100 down to 16.
This list contains four groups of 4 increasing subsequences and also decreasing:
4 3 2 1 / 8 7 6 5 / 12 11 10 9 / 16 15 14 13
The slashes are added to show groups of 4.
The decreasing subsequences are obvious: 4 3 2 1 etc...
The increasing subsequences can be formed by taking one member of each group of 4.  (It doesn't matter which)

To answer the original problem create 100 numbers would go
10 9 8 7 6 5 4 3 2 1 20 19 ... 82 81 100 99 98 97 96 95 94 93 92 91

The 20 decreasing subsequences are again obvious
The 20 increasing subsequences could be
10 20 30 40 50 60 70 80 90 100
9 19 29 39 49 59 69 79 89 99
...
1 11 21 31 41 51 61 71 81 91

  Posted by Jer on 2016-02-11 11:56:25
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