MathDB

In the beginning, there are

100

cards on the table, and each card has a positive integer written on it. An odd number is written on exactly

43

cards. Every minute, the following operation is performed: for all possible sets of

3

cards on the table, the product of the numbers on these three cards is calculated, all the obtained results are summed, and this sum is written on a new card and placed on the table. A day later, it turns out that there is a card on the table, the number written on this card is divisible by

2^{2018}.

Prove that one hour after the start of the process, there was a card on the table that the number written on that card is divisible by

2^{2018}.

Problem Statement