2024 AIME II Problems/Problem 3
Contents
[hide]Problem
Find the number of ways to place a digit in each cell of a 2x3 grid so that the sum of the two numbers formed by reading left to right is , and the sum of the three numbers formed by reading top to bottom is . The grid below is an example of such an arrangement because and .
Solution 1
Consider this table:
We note that , because , meaning it never achieves a unit's digit sum of otherwise. Since no values are carried onto the next digit, this implies and . We can then simplify our table into this:
We want , or , or . Since zeroes are allowed, we just need to apply stars and bars on , to get . ~akliu
Video Solution
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
See also
2024 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
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