2017 AIME II Problems/Problem 4
Problem
Find the number of positive integers less than or equal to whose base-three representation contains no digit equal to .
Solution
The base- representation of is . Because any -digit base- number that starts with and has no digit equal to must be greater than , all -digit numbers that have no digit equal to must start with or in base . Of the base- numbers that have no digit equal to , there are -digit numbers that start with , -digit numbers that start with , -digit numbers, -digit numbers, -digit numbers, -digit numbers, -digit numbers, and -digit numbers. Summing these up, we find that the answer is .
See Also
2017 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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