We wish to lay down boards on a floor with width B in the direction across the boards. We have n boards of width b, and B/b is an integer, and nb≤B. There are enough boards to cover the floor, but the boards may have different lengths. Show that we can cut the boards in such a way that every board length on the floor has at most one join where two boards meet end to end.
https://cdn.artofproblemsolving.com/attachments/f/f/24ce8ae05d85fd522da0e18c0bb8017ca3c8e8.png combinatoricscombinatorial geometry