MathDB

6

Part of 1987 Swedish Mathematical Competition

Problems(1)

a baker with access to a number of different spices bakes ten cakes

Source: 1987 Swedish Mathematical Competition p6

3/28/2021
A baker with access to a number of different spices bakes ten cakes. He uses more than half of the different kinds of spices in each cake, but no two of the combinations of spices are exactly the same. Show that there exist three spices a,b,ca,b,c such that every cake contains at least one of these.
combinatorics