11 squared is 121
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4
To find the two-digit numbers whose digits sum to a perfect square, we first identify the possible sums of the digits, which range from 1 (1+0) to 18 (9+9). The perfect squares in this range are 1, 4, 9, and 16. The valid two-digit combinations for these sums are: for 4 (14, 23, 32, 41, 50), for 9 (18, 27, 36, 45, 54, 63, 72, 81, 90), and for 16 (79). Counting all valid combinations gives us a total of 20 two-digit numbers.
16
Six: 0, 1, 4, 5, 6 and 9
There are numbers that will meet these requirements but no such digits.