+0

0
42
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+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.

Feb 17, 2022

#1
+1384
+1

The 4th clue alone narrows down the number to 68 possibilities, but we can not go any farther, because the question is incomplete.

Feb 17, 2022
#2
+18
+1

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.

Feb 17, 2022
#3
+1384
+1

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.

BuilderBoi  Feb 17, 2022
edited by BuilderBoi  Feb 18, 2022
#4
+18
0
`Thanks so much!`
Feb 18, 2022
edited by Peakpine1  Feb 18, 2022