Сonstructive problems and optimization
5. Find a two-digit number equal to the sum of the first digit and the square of the second digit. 6. In three digits, they crossed out the second digit, as a result of which it decreased 6 times. Find the original number. 7. A three-digit number crossed out the number of hundreds, as a result, the number decreased by 7 times. Find the original number. 8. Find two two-digit numbers, the cube of one of which is equal to the square of the other. 9. The sum of several numbers is 1, and each of them is less than 1. Can the sum of their cubes be more than 1? 10. Find a two-digit number equal to the sum of the first digit and the square of the second digit. 11. In three digits, they crossed out the average number, as a result of which it decreased 6 times. Find the original number. 12. A three-digit number crossed out the number of hundreds, as a result, the number decreased by 7 times. Find the original number. 13. Find two two-digit numbers, the cube of one of which is equal to the square of the other. 14. The sum of several numbers is 1, and each of them is less than 1. Can the sum of their cubes be more than 1?