Difference between revisions of "2001 AIME II Problems/Problem 1"
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
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Latest revision as of 20:34, 4 July 2013
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 
.
.
, 
.
.
, 
.
, 
.
. 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) | ||
| Preceded by First question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
