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.
(In reply to
proof on the internet (spoiler) by Charlie)
Actually, I find the puzzle itself difficult to follow.
On my bookshelf I have the tenvolume set of K.Sengupta's collected problems. As is well known, by some whimsy of the author, each volume has a real number 1.x, 2.x, 3.x, etc. We shall call these 1,2,3.. for short.
Assume I order them: 1,10,2,9,3,8,4,7,5,6. I see no continuous subsequence of four here which is either strictly increasing or decreasing.
But if the subsequence can be noncontinuous, e.g. we can rub out 10, and select 1,2,3,4 as our fourpart sequence, then a more challenging problem (by far) is to arrange volumes 1 to 9 in some order such that there is no noncontinuous sequence of four that is either strictly increasing or strictly decreasing, given that either is acceptable.
Edited on January 29, 2016, 7:47 am

Posted by broll
on 20160129 07:37:57 