Which perfect square of a 4-digit number has the same last four digits as the original number?
Solution
9376
Start with the last digit: only numbers ending in 0, 1, 5, and 6 can produce a perfect square also ending in the same digit.
Knowing this, then look at just the last two digits: only numbers ending in 00, 01, 25, or 76 can produce a perfect square also ending in the same digit.
Using the same logic, then last three digits must be 000, 001, 625, or 376.
Finally, the last four digits must be 0000, 0001, 0625, or 9376. Since a four-digit number cannot start with a zero, the unique solution is 9376.
One reply on “Four Digits Squared”
0’0001×’0001=00000001