MathDB

There are

200

boxes on the table. In the beginning, each of the boxes contains a positive integer (the integers are not necessarily distinct). Every minute, Alice makes one move. A move consists of the following. First, she picks a box

X

which contains a number

c

such that

c = a + b

for some numbers

a

and

b

which are contained in some other boxes. Then she picks a positive integer

k > 1

. Finally, she removes

c

from

X

and replaces it with

kc

. If she cannot make any mobes, she stops. Prove that no matter how Alice makes her moves, she won't be able to make infinitely many moves.

Problem Statement