1987 AIME Problems/Problem 1
Problem
An ordered pair of non-negative integers is called "simple" if the addition in base requires no carrying. Find the number of simple ordered pairs of non-negative integers that sum to .
Solution
Since no carrying over is allowed, the range of possible values of any digit of is from to the respective digit in (the values of are then fixed). Thus, the number of ordered pairs will be .
If you do not understand the above solution, consider this. For every positive integer , there is only one whole number that you can add to it to obtain the required sum. Also, the total number of non-negative integers that are smaller than or equal to an integer is because there are positive integers that are less than it, in addition to and itself.
See also
1987 AIME (Problems • Answer Key • Resources) | ||
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Followed by Problem 2 | |
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