Travis Hale

Again, the riddle:



A paper company sells reams of paper in boxes of 6, 9, and 20 reams. What is the largest number of reams that cannot be delivered in full boxes?

The Answer:

43. Using the 6 ream box and 9 ream box, the company can deliver any number of reams that is divisible by 3, 6 or larger – 6, 9, 12, 15, and so on. If an order comes in for a number of reams greater than 20 that is not divisible by 3, the company can include boxes of 20, subtracting 20 from the total until the remaining part of the order calls for a number of reams divisible by 3. This strategy covers every number greater than 43. (44 – 20 = 24, which is divisible by 3; 45 is divisible by 3; 46 – 20 – 20 = 6, which is divisible by 3; 47 – 20 = 27 which is divisible by 3; 48 is divisible by 3; and so on.