MathDB

There are

n

matches lying on a table, forming

n

one-match piles. Adam wants to combine them into a single pile of

n

matches. He will do this using

n-1

operations, each of which consists of combining two piles into one. Adam has made a deal with Bartek that every time he combines a pile of

a

matches with a pile of

b

matches, he will receive

a\cdot b

candies from Bartek. What is the greatest number of candies that Adam can receive after performing

n-1

operations? Justify your answer.

Problem Statement