Question

Find the unique four-digit integer n with these properties:

The last digit (the units digit) of n is 9.
The digits of n add up to 27.
Two digits of n are the same.
n is a perfect square.

Answer 1

I believe the answer is 3,969

Answer 2

3,969

Explanation:

If n is a perfect square, then the last digits of the prefect square must be 3 or 7 because n ends in 9.

Since n is 4 digits the number can only land between 33 and 97.

(33, 37, 43, 47, 53, 57, 63, 67, 73, 77, 83, 87, 93, 97)

squared- 1089, 1369, 1849, 2209, 2809, 3249, 3969, 4486, 5329, 5939, 6889, 7569, 8649, 9409

possible answers- 2209, 3969, 4486, 5939, 6889, 9409

2+2+0+9 = 13

3+9+6+9 = 27

4+4+8+6 = 22

5+9+3+9 = 26

6+8+8+9 = 31

9+4+0+9 = 22