33rd Eötvös Competition Problems 1929

1.  Coins denomination 1, 2, 10, 20 and 50 are available. How many ways are there of paying 100? 2.  Show that ∑i=0 to k nCi (-x)i is positive for all 0 ≤ x < 1/n and all k ≤ n, where nCi is the binomial coefficient.