Changing an order
Source: http://www.olimpiadamatematica.es/platea.pntic.mec.es/_csanchez/olimp_1963-2004/OME2004.pdf
November 14, 2016
combinatorics
Problem Statement
A table with 1000 cards on a line, numbered from 1 to 1000, is considered. The cards are ordered in the usual way. Now, we proceed in the following way.The first card (which is 1) is put just before the last card (between 999 and 1000) and, after, the new first card (which is 2) is put after the last card (which was 1000). Show that after 1000 movements, the cards are ordered again in the usual way. Show that the analogous result ( movements for cards) does not hold when is odd.