MathDB
persons exchanging coins around a table

Source: Nordic Mathematical Contest 2000 #2

October 3, 2017
combinatoricsInteger sequence

Problem Statement

The persons P1,P2,...,Pn−1,PnP_1, P_2, . . . , P_{n-1}, P_n sit around a table, in this order, and each one of them has a number of coins. In the start, P1P_1 has one coin more than P2,P2P_2, P_2 has one coin more than P3P_3, etc., up to Pn−1P_{n-1} who has one coin more than PnP_n. Now P1P_1 gives one coin to P2P_2, who in turn gives two coins to P3P_3 etc., up to Pn Pn who gives n coins to P1 P_1. Now the process continues in the same way: P1P_1 gives n+1n+ 1 coins to P2P_2, P2P_2 gives n+2n+2 coins to P3P_3; in this way the transactions go on until someone has not enough coins, i.e. a person no more can give away one coin more than he just received. At the moment when the process comes to an end in this manner, it turns out that there are two neighbours at the table such that one of them has exactly five times as many coins as the other. Determine the number of persons and the number of coins circulating around the table.
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