1. We call a positive integer squareful if every two adjacent digits in the number form a square. The number 364 is, for example, squareful, because both 36 and 64 are squares.

How many digits does the largest squareful number have?
A) 2
B) 3
C) 4
D) 5
E) 6
A1. D) 5 The squares of two digits are $16, 25, 36, 49, 64$, and 81. We start with each of these squares and look for which digit we can append so that the last two digits also form a square. For example: after 16, a 4 can be appended because of 64 (and no other digit can follow the 6), then comes a 9 to form 49, and then it stops because no square starts with a 9. With the six different starting squares, you can form the following numbers at most:

- 1649
- 25
- 3649
- 49
- 649
- 81649

The largest number from this list, 81649, consists of five digits.