+18 Find the unique four-digit integer with these properties:
The last digit (the units digit) of is .
The digits of add up to .
Two digits of are the same.
is a perfect square.
+2668 Your question isn't fully complete.
The 4th clue alone narrows down the number to 68 possibilities, but we can not go any farther, because the question is incomplete.
+18 Let me write it again
Find the unique four-digit integer with these properties:
The last digit (the units digit) of this four digit number is 9 .
The digits of the this four digit number add up to 27.
Two digits of this four digit number are the same.
is a perfect square.
+2668 Ok, now it is solvable. The first clue narrows the options down to 14 options: 1089, 1369, 1849, 2209, 2809, 3249, 3969, 4489, 5329, 5959, 6889, 7569, 8649, 9409.
After looking through all the possible options, we can narrow down our list furthur (the number must have 2 of the same digits) : 2209, 3969, 4489, 5959, 6889, 9409.
Looking through the list again, we see that only \(\color{brown}\boxed {3969}\) satisfies all 4 conditions.
