You're going to compete in a standoff math-flash cards shootout tomorrow in your math class. The rules are that you and your opponent will be given a flash card to look at and you need to give the answer before your opponent. The flash card has a subtraction problem with the form x-y where x and y are each between 1 and 9. You must quickly give the difference of those two numbers.
The caveat is that if x<y, add 10 to x before subtracting y (so that the difference remains between 1 and 9). What is the minimum number of subtraction problems that you must learn to guarantee that you will be able to answer all possible subtraction problems?
--- Diluted restatement of the problem --
Let 'x' and 'y' be a number between 1 and 9. Suppose you wanted to take the difference (x-y) but you need to "borrow" (that is add 10 to x) whenever x<y before taking (x-y) -- this guarantees that x-y is a number between 1 and 9. What is the minimum number of combinations of subtraction problems involving x and y (for x,y each between 1 and 9) that you must learn to be able to answer ALL problems involving those x and y?
i.e., If I had asked how many combinations were necessary to answer ALL subtraction problems x-y where x=9 and 'y'= is between 1 and 9, the answer is 9.
Can you beat 54 ?