MathDB

Given a paper on which the numbers

1,2,3\dots ,14,15

are written. Andy and Bobby are bored and perform the following operations, Andy chooses any two numbers (say

x

and

y

) on the paper, erases them, and writes the sum of the numbers on the initial paper. Meanwhile, Bobby writes the value of

xy(x+y)

in his book. They were so bored that they both performed the operation until only

1

number remained. Then Bobby adds up all the numbers he wrote in his book, let’s call

k

as the sum.

a

. Prove that

k

is constant which means it does not matter how they perform the operation,

b

. Find the value of

k

Problem Statement