2001 AIME II Problems/Problem 1
Problem
Let be the largest positive integer with the following property: reading from left to right, each pair of consecutive digits of forms a perfect square. What are the leftmost three digits of ?
Solution
The two-digit perfect squares are . We try making a sequence starting with each one:
- . This terminates since none of them end in a , giving us .
- .
- , .
- .
- , .
- , .
The largest is , so our answer is .
See also
2001 AIME II (Problems • Answer Key • Resources) | ||
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Followed by Problem 2 | |
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