Two gamblers, A and B, divided into a few bundles the money they've recently won and agreed to toss a coin for each bundle.
A 3rd gambler, nicknamed Mathwiz remarked: "It is an even money that A will win at least five of the tosses".
How many bundles of money were there?

this solution can be derived from the property that the sum of the n'th row of pascals triangle is 2^n.  Now, if there are n piles, then we need for the sum of the 5th through n'th element of the n'th row to sum to 2^(n-1) or exactly half the total.  Now, because Pascal's triangle is symetric and the n'th row has n+1 elements (0 thru n), then we need n+1 to be even and thus n to be odd.  Since we are starting the sum at 5, then we also need for that to be the start of the second half.  So in other words, we need (n-5+1)*2=n+1
2n-10+2=n+1
n=9
thus there must be n piles. 

Posted by Daniel on 2011-12-31 08:28:16