+0  
 
0
99
4
avatar+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
avatar+2455 
0

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.

 Feb 17, 2022
 #2
avatar+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
avatar+2455 
0

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
avatar+18 
0
Thanks so much!
 Feb 18, 2022
edited by Peakpine1  Feb 18, 2022

28 Online Users

avatar