Wikipedia:Reference desk/Archives/Mathematics/2013 March 16

= March 16 =

IMO problem
1)show that out of any 5 points chosen within a square of side length 2 there are two whose distance apart is at most √2

2)Find the remainder when 2^1990 is divided by 1990.

Solomon7968 (talk) 14:55, 16 March 2013 (UTC)


 * 1) The configuration of the square will be:

*---*   |       |    |   *   |    |       |    *---*


 * You can use some basic trig from there to show the result. StuRat (talk) 16:54, 16 March 2013 (UTC)


 * Can you prove that there is no other configuration with wider separation? What about an inscribed pentagon, for example? Looie496 (talk) 17:49, 16 March 2013 (UTC)


 * Right. StuRat's claim is not a proof. You're going to need to use the pigeonhole principle for this. —Bkell (talk) 20:07, 16 March 2013 (UTC)


 * 1)Divide the square to 4 subsquares, each one with side length 1, then there must be two points on the same subsquare therefore the distance between them is at most square root of 2.
 * 2)Factor 1990, and use Chinese remainder theorem and Fermat's little theorem --84.229.98.135 (talk) 20:14, 16 March 2013 (UTC)

I've added a space to the original question, as "atmost" looked like "almost". 86.186.142.172 (talk) 09:32, 17 March 2013 (UTC)

In my opinion, there's no way either of these could have been an IMO problem. 64.140.122.180 (talk) 09:55, 17 March 2013 (UTC)

Pollution
what is pollution how it is caused what is the 4 types of pollution — Preceding unsigned comment added by 190.80.8.6 (talk) 21:49, 16 March 2013 (UTC)


 * This is the mathematics reference desk. This is probably not the appropriate place to ask your question. You might try the science reference desk. —Bkell (talk) 21:54, 16 March 2013 (UTC)