Problem number 24. Anne replaces letters in the calculation K-A-N plus G-A minus R-O-O with some of the numbers from 1 to 9 and then calculates the result. The same letters are replaced by the same numbers and different letters by different numbers. What is the largest possible result she can get? A, 925. B, 933. C, 939. D, 942. E, 948. George, do you have a hint for us as to how to solve this problem? To get the largest result, make the numbers you are adding together as large as possible and the one you are subtracting as small as possible. Also, pay attention to the place value. The numbers that we are adding together are K-A-N and G-A. These are the ones that we want to make as large as possible. R-O-O is the number we are subtracting, and that's the one we want to make as small as possible. It's fairly obvious that to make R-O-O as small as possible, we need to use the 1 for the hundredth digit and then use 2 to replace the two O's. So the number we will subtract will be 122. To make K-A-N plus G-A as large as possible, we will use 9 as the hundredth digit, so that will replace K. And then notice that A occurs both in the tenths digit and in the ones digit. One option that we have is to make A, 8, both in this number and in this one, and then G, the other tenths digit, would be 7, and N would be 6. The other option is K is still 9, G is 8, and then A is 7, and N is 6. Let's add those and see which one gives us a bigger sum. 6 plus 8 is 14, carry the 1, 8 plus 7 is 15, and 1 more is 16, carry the 1, get 1,064. The other sum would be 6 plus 7 is 13, 7 plus 8 is 15, and 1 more is 16, 9 plus 1 is 10, 1,063. The larger sum is 1,064, so we will take this number and subtract 122 from it. 4 minus 2 is 2, 6 minus 2 is 4, 10 minus 1 is 9. So we get answer D, 942, as the largest possible result.

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