Question

In: Advanced Math

You're cleaning up your little nephew's toy room. There are T toys on the floor and...

You're cleaning up your little nephew's toy room. There are T toys on the floor and n empty toy storage boxes. You randomly throw toys into boxes, and when you're done the box with the most toys contains N toys.

(a)What is the smallest that N could be when T=2n+1?

(b) What is the smallest that N could be when T=kn+1?

(c)Now suppose that the number of toys T satisfies

T<n(n−1)/2.

Prove that when you are done cleaning there will be (at least) one pair of boxes that contain the same number of toys.

Solutions

Expert Solution

Colby Messinger answered 2 years ago
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