Question 137
Initially, we put 100 cards on a table, each containing a positive integer. Exactly 28 of these cards contain odd numbers. Then, on each minute the following operation has been performed. We compute the product of numbers on every set of 12 cards on the table, add up all these products, write this number onto a new card and put this card onto the table. Is it possible to choose initial 100 numbers so that for every positive integer $d$ the table will eventually contain some card with a number divisible by $2^d$? (I. Bogdanov)