Scrutiny (Posted on 2023-05-01)

	Submitted by Ady TZIDON
Rating: 5.0000 (1 votes)
Solution:	(Hide)
Of the n planets , assume that two watch each other. If any of the remaining n – 2 astronomers are looking at one of these planets, then there won’t be enough astronomers left to observe all the remaining n – 2 planets. On the other hand, if none of the remaining astronomers are looking at the two closest-set planets, then we can discard those two and ask our original question of the n – 2 planets that remain: Which two are closest together? Again, those two astronomers must be observing each other. And so on. Each time we discard a pair of planets we’ll have some odd number remaining. But that number can’t decrease forever (it can’t be negative). We must eventually arrive at 1, a planet that no astronomer is observing.

	Subject	Author	Date
	My version	broll	2023-05-02 11:36:51
	proof by contradiction	xdog	2023-05-02 10:14:55
	A start, but incomplete	Larry	2023-05-01 23:42:39
	re(2): soln	Steven Lord	2023-05-01 19:24:27
	re: soln	Kenny M	2023-05-01 17:28:04
	soln	Steven Lord	2023-05-01 16:34:21