7.1. (14 points) We will call a natural number a snail if its representation consists of the representations of three consecutive natural numbers, concatenated in some order: for example, 312 or 121413. Snail numbers can sometimes be squares of natural numbers: for example, $324=18^{2}$ or $576=24^{2}$. Find a four-digit snail number that is the square of some natural number.
Answer: 1089.

Solution. Note that a snail number can only be a four-digit number if the three numbers from which its record is formed are $8, 9, 10$ (numbers $7, 8, 9$ and smaller still form a three-digit number, while $9, 10, 11$ and larger - already form a number of no less than five digits). It remains to figure out the order of the selected numbers. The square of a natural number cannot end in 10 (there should be an even number of zeros or none at all). Also, a square cannot end in the digit 8. Therefore, the last digit must be 9. The remaining options are 8109 and 1089. Since $8109=90^{2}+9$ and $1089=33^{2}$, the only four-digit snail number that is a square is 1089.