Sample Problem

In a box, there are 10 marbles marked from 1-10. On his first turn, Tom takes out a certain number of marbles whose sum is X; his second turn, he takes out another number of marbles whose sum is 2X; the third turn, the sum of the marbles he removes is 4X. If he took out 9 marbles so far, what is the number of the remaining marble in the box?



The sum of the 9 marbles’ numbers is X + 2X + 4X = 7X. Since the sum of all those 10 numbers is 1 + 2 + ⋯ + 10 = 55 and 55 ÷ 7 = 7 R6, X could be 7 with the remaining marble being number 6.