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Erase the right 90 (Posted on 2016-01-28) Difficulty: 3 of 5
101 distinct real numbers are written in any order

Prove that it is possible to erase 90 of them leaving a sequence of 11 numbers that are in either a strictly increasing or strictly decreasing order.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

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re: Sequence? Comment 5 of 5 |
(In reply to Sequence? by Jer)

In order to be assured of being able to leave n+1 in order, there must be n^2 + 1 numbers originally. In the present case n = 10, so that n+1 = 11 and n^2+1 = 101.  For, say, being assured of 10 that are monotonic, n = 9 and you'd need 82 originally (taking away 73).  Those numbers don't jibe with A241720, as the number prior to 101 should be 82.
  Posted by Charlie on 2016-01-29 11:33:30

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