2019 AIME I Problems/Problem 1
Problem 1
Consider the integer Find the sum of the digits of
.
Solution
Let's express the number in terms of . We can obtain
. By the commutative and associative property, we can group it into
. We know the former will yield
, so we only have to figure out what the last few digits are. There are currently
1's. We know the last 4 digits are 1110, and that the others will not be affected if we subtract
. If we do so, we get that
. This method will remove 3 1's, and add a 7, 8 and 9. Therefore, the sum of the digits is
.
-eric2020
See Also
2019 AIME I (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
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All AIME Problems and Solutions |
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