Philpot Nerdling collects baseball cards and keeps them in a three-ring binder. Rather than regular pages made of paper, the binder contains plastic sleeves that are large enough to hold nine cards per page, arranged in a 3×3 grid. Cards numbered 1 through 9 are on the first page, 10 through 18 on the second page, and so forth.
Philpot has just started collecting for this season, and the first card he finds is numbered “258”. Philpot managed to locate the proper page, but couldn’t remember which of the nine spaces should contain the card.
Without using division or subtraction, can you help him locate the right space?
Answer
The card should go in the sixth spot. Adding all the digits of a 10-base number together will give you a number from 1 to 9, which corresponds to the lowest digit in the 9-base system to which you’re converting.
In other words, 2+5+8 = 15, and 1+5 = 6. The card goes in the sixth spot.