The January Math Challenge had three parts:
Part I: Express as many of the perfect squares less than 1,000 as the sums of two or more consecutive integers as possible. Example: 9 = 4 + 5
Part II: The sequence 2, 3, 5, 6, 7, 8, 10, 11 consists of all positive integers that are not perfect squares. What is the 500th term of the sequence?
Part III: Find the largest positive integer such that each pair of consecutive digits forms a perfect square. Example: The number 364 is made up of the perfect squares 36 and 64.
Saperstein and Song both said it was easy.
"Then why don't you answer it and get a bag of M&M's?" Alex asked.
"Because we helped make it up."
Assume that in Part I, "consecutive integers" means "consecutive positive integers". There should also be an ellipsis ("...") after the 11 in Part II, to indicate the series continues indefinitely.
See how well you do on the "January Math Challenge".