Number Solitaire

735 7 + 3 + 5 = 15 7 x 3 x 5 = 105 735 ÷ 15 = 49 4 + 9 + 7 + 3 + 5 = 28 8 – 2 = 6 I’ve now generated all digits 0 1 2 3 4 5 6 7 8 9 from 735 Nothing of any mathematical significance here. But next time you’re on the subway, instead of playing suduko or a portable PS2 blaring sound effects without headphones (what are those people thinking?), take a three-digit number and try to derive all 10 digits using basic operations of addition, subtraction, multiplication, and division of only the digits of the numbers and the whole numbers you’ve generated thus far. And stick to whole and positive numbers. I just made this game up. A few more rules:

• You have to use all the digits in a number or none of the digits. That is, to use 351, you have to use 3 + 5 + 1 or 351, not just 3 + 5 or 51, and so forth.
• Each step must yield at least one new digit.
• You can’t reuse the a number within the same step. That is, each step adds a whole number to your pool. You can use each number within your pool no more than once per step.
• You cannot use more than two whole numbers from your pool within the same step.

Let’s try another: 111 1 + 1 + 1 = 3 111 ÷ 3 = 37 37 + 3 = 40 37 x 40 = 1,480 1,480 x 37 = 54,760 5 + 4 + 7 + 6 + 0 = 22 0 1 2 3 4 5 6 7 8 9 Aim for the fewest number of steps! Anyway, this is a boring game. It could come in useful, though, like in jury duty.