Math Answers My son (14) asked how [Magic Gopher] works. He tried several times to stump them, with no luck. He wanted to know he mathematical method for "guessing" the numbers. I'm sure it's a very simple and logical process, but I have no answer. Can anyone help? Thanks. Joyce knows! It's the magic of our base 10 system :-) Basically what you're doing is eliminating the second digit and then subtracting the first digit from 10 times the first digit which always give 9 times the first digit. On the Egyptian chart at the end, all the multiples of 9 always have the same symbol next to them. [Sandra note: All except the nines are just random dummy-art because only the multiples of nine will be "the answer." The program changes the symbols on the chart each time you play the game.] Algebraically it goes like this ... If a number looks like ab, it would be represented algebraically as: 10*a + b. So for: 12 then a=1 and b=2 so 12=10*1 + 2 37 then a=3 and b=7 so 37=10*3 + 7 82 then a=8 and b=2 so 82=10*8 +2 In the first step of the game they ask you to add a and b together. And then they tell you to subtract that number from the original number. That's just a way of eliminating the last digit so all problems turn into: 10*a + b - (a+b) rearranging, you can see that the b part of every 2 digit number gets eliminated: 10*a - a + b - b So all problems turn into either 10-1, 20-2, 30-3, 40-4 ... 10*a - a = 9a 10*1 - 1 = 9*1 = 9 10*2 - 2 = 9*2 = 18 10*3 - 3 = 9*3 = 27 and so on. So all two digit numbers are turned into 9 times the first digit of the number. Joyce More math games and ideas