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 possible pairs of consecutive digits are , and . Choosing as the leftmost pair of digits would yield as the greatest number with the requested property. Similarly, would yield would yield would yield would yield , and would yield . Of these, is the largest, and the leftmost three digits are .
The problems on this page are the property of the MAA's American Mathematics Competitions