Car Number Puzzle

Find the Car Number

Three friends were returning from college when they saw a speeding car hitting a man while he was crossing the road and fleeing away. They shouted in desperateness  to seek help from the passerbyes but failed.

In the meantime they noticed the registration number of the car and tried to remember in their own style. They rushed the person to the nearby hospital where he was admitted. The doctor called the police as this was a case of road accident and a case was registered. 

In order to do proper investigation the police started inquiring the three friends and asked them if they could provide the registration number of car so that the driver who had hit the person can be caught up. All the three friends tried a lot to remember the car number but failed so they altogether decided to zero upon the number of the car as they have remembered the car number with some mathematical properties behind it.

1^st Student: -- Sir, the first two digits of car number were same.

2^nd Student: - Sir, the last two digits of car number were same.

3^rd Student:- The four digit number is a  square number.

Can you guess the car number to help the police to nab the guilty?

Send me your valuable comments on rkthakur1974@gmail.com and try to reason this out with algebraic proof ? See you next day till then open up your mind.

Ans :- 7744