MathDB

Let

n

and

k

be positive integers. Chef Kao cuts a circular pizza through

k

diameters, dividing the pizza into

2k

equal pieces. Then, he dresses the pizza with

n

toppings. For each topping, he chooses

k

consecutive pieces of pizza and puts that topping on all of the chosen pieces. Then, for each piece of pizza, Chef Kao counts the number of distinct toppings on it, yielding

2k

numbers. Among these numbers, let

m

and

M

being the minimum and maximum, respectively. Prove that

m + M = n

Problem Statement