SOLUTION: Three students of mathematics were out for a stroll when they noticed a car going at great speed broke the traffic regulations. None of the students noticed the four digit number o

Question 709195: Three students of mathematics were out for a stroll when they noticed a car going at great speed broke the traffic regulations. None of the students noticed the four digit number on the license plate; but being mathematicians they noticed some peculiarities about the number.
One recalled that the first two digits were the same. Second recalled that the last two digits were also alike. And finally the third student said that the four digit number was a perfect square.
This information was enough to find out the number on the license plate. What is the four digit number on the license plate?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
We can represent the 4 digit number as aabb.
The number can be written as 1000a + 100a + 10b + b, and this number is a perfect square:
N = 1100a + 11b = 11(100a + b)
So the number must be a multiple of 11
The multiples of 11 which result in 4 digit numbers are 33, 44, 55, 66, 77, 88 and 99
Of these, only one fills the requirement: 88^2 = 7744
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