How many numbers 10 through 87 have the sum of their digits equal to a perfect square?

Answer 1

To find the numbers between 10 and 87 with the sum of their digits equal to a perfect square, we need to consider each number individually. The perfect squares between 1 and 9 are 1, 4, and 9. For each perfect square, we can list the numbers that meet the criteria:

1. For the perfect square 1, the numbers are 10, 19, 28, 37, 46, 55, 64, 73, 82.
2. For the perfect square 4, the numbers are 40, 49, 58, 67, 76, 85.
3. For the perfect square 9, the numbers are 90.

Therefore, there are 14 numbers between 10 and 87 that have the sum of their digits equal to a perfect square.

Answer 2

Numbers whose digits add to a perfect square between 10 and 87 are:

10 = 1 + 0 = 1 = 12
13 = 1 + 3 = 4 = 22
18 = 1 + 8 = 9 = 32
22 = 2 + 2 = 4 = 22
27 = 2 + 7 = 9 = 32
31 = 3 + 1 = 4 = 22
36 = 3 + 6 = 9 = 32
40 = 4 + 0 = 4 = 22
45 = 4 + 5 = 9 = 32
54 = 5 + 4 = 9 = 32
63 = 6 + 3 = 9 = 32
72 = 7 + 2 = 9 = 32
81 = 8 + 1 = 9 = 32

This is a total of 13 numbers.

* * * * *

And also

79 = 7 + 9 = 16 = 42

So a total of 14 numbers.

Answer 3

2