A local charity runs a lottery to raise funds, similar to some states' lotteries. A player chooses M distinct numbers from 1 to N on each ticket he buys, hoping that some or all on some ticket will match the ones drawn on stage.

After some time, the charity changed the game a little -- they increased by 1 the amount of numbers to be chosen on a ticket (M in this case), while keeping N (the total possible numbers) the same as to minimize confusion.

One participant in the old game always bought one card for every combination without any consecutive numbers. In order to maintain this practice in this new game, our punter had to buy exactly one and a half times as many tickets as before.

• How many numbers were on each ticket? (N)
• How many numbers had to be selected before the change in rules? (M) ... after the change? (M+1)
• How many tickets did our player buy each drawing before the rule change? ... after the rule change?

using mathematica I found this solution

N=14  M=3

thus the participant first picked 220 combinations and then after the change to M=4 picked 330 and 330=1.5 * 220.

Posted by Daniel on 2008-05-01 19:04:13