The first number on each card is a power of 2 (2,4,8,16,32). Every natural number up to 63 is a sum of some of these numbers (just write it in base 2). The rest of the numbers on each card are chosen precisely to make this work: on the card whose first number is 2, the numbers appearing are exactly those whose binary expression has a 1 in th th position. How high the numbers go on each card is irrelevant, as long as the upper bound is the same on each one
All you need do is add up the top left hand number on each of these cards. This will be the number they chose.