A 4 digit number when squared, the last 4 digits of the square are same as that of the original number. Find the sum of digits of this number.

Solution (By Examveda Team)

Answer : 25

we done this question by back tracking rule we start from single digits such as 1,2,3,4,5,6,7,8,9 and we got the square of 1 , 5 and 6 last digit is same as original digit.

such as square of 1 is 1 , square of 5 is 25 and square of 6 is 36.

After that we start with two digits series that end by 1, 5 and 6.

Such as 11, 21,31 ..., 91.

And 15, 25, 35 ...., 95.

And 16, 26, 36 .... , 96.

And we got a square of 25 and 76 last digit is same as original digit.

After that we start with three digits series that end by 25 and 76.

Such as 125, 225,325 ..., 925.

And 176, 276, 376 ...., 976.

And again we got a square of 625 and 376 last digit is same as original digit.

After that we start with three digits series that end by 25 and 76.

Such as 1625, 2625,3625 ..., 9625.

And 1376, 2376, 3376 ...., 9376.

And we got a square of 9376 last digit is same as original digit. So number is 9367.

And its sum is 25.

We know its not a got method to do this as soon as we found the any method to solve this problem we will publish on our we page.

Thank you to posting such good question