MATHS PUZZLE # 2 First Leg of Second Year

MATHS PUZZLE # 2 FIRST LEG --Second Year of the Project-- (from the 11th to the17th of October 2010  -submitted by the 18th)

 A ROAD HOG

 A reckless driver was driving his vehicle and speaking on his mobile phone at the same time. That’s why he caused an accident. The guy fled but the three passengers travelling in the car he had the crash in managed to see part of the reckless driver’s car number plate. 
Eduard, the one who was driving, remembered that the first two digits of the guy’s number plate were the same number. Sergi, who was sitting next to the driver, remembered that the last two digits were also the same number. Behind them in the car was Carla, a young girl who was mad keen on Mathematics. She said that the guy’s number plate had four digits and that it was a perfect square.

Find out the risky driver’s number plate.
You can send the answers to FernandoEscuin@iescampanar.com

SOLUTION
A possible solution is:

The numbers which once squared are a 4-digit figure can only be those between 32 and 99.

On the other hand just because of the divisibility rules, these squared numbers are multiple of 11 since the odd digits sum as much as the even ones. Possible numbers are: 

33² = 1089

44² = 1936

55² = 3025

66² = 4356

77² = 5929

88² = 7744

99² = 9801

The only solution then is 7744 (The first two digits are the same and also the last two)