2004 AMC 12B Problems/Problem 25
Problem
Given that is a -digit number whose first digit is , how many elements of the set have a first digit of ?
Solution
Given digits, there must be a power of with digits such that the first digit is . Thus contains elements with a first digit of . For each number in the form of such that its first digit is , then must either have a first digit of or , and must have a first digit of . Thus there are also numbers with first digit either or . By using complementary counting, there are elements of with a first digit of . Now, has a first of if and only if the first digit of is , so there are elements of with a first digit of .
See also
2004 AMC 12B (Problems • Answer Key • Resources) | |
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All AMC 12 Problems and Solutions |