Charlie's house number is a square of 3 digits. This number when reversed is also a square and is Charlie's telephone extension at work. His car registration number is a square of 4 digits and is formed from his house number by repeating the right hand digit.

What is Charlie's house number?

A solution

The following solution was offered by Trevor of Riccarton High School, Christchruch, New Zealand. Other correct solutions were received from Andrei (School 205, Bucharest), Mary (Birchwood Community High School), Rachel and Sebastian (Hethersett High School) and Claire.

Well first, I found all three digit numbers which are square numbers...

10^{2} = 100

11^{2} = 121

12^{2} = 144

13^{2} = 169

14^{2} = 196

15^{2} = 225

16^{2} = 256

17^{2} = 289

18^{2} = 324

19^{2} = 361

20^{2} = 400

21^{2} = 441

22^{2} = 484

23^{2} = 529

24^{2} = 576

25^{2} = 625

26^{2} = 676

27^{2} = 729

28^{2} = 784

29^{2} = 841

30^{2} = 900

31^{2} = 961

...then I searched for pairs of square numbers that when one is reversed, it will be the same as the second, but not including paladromic numbers...

pairs: 144, 441

169, 961

...then the final clue is that Charle's car registration number is a four digit number which is also a square number
as well, and is formed by repeating the last digit of the house number, and using the numbers which I have picked...

1444, 4411
1699, 9611

...I can pick a square number from here, if there is one......1444 is a square of 38! So that means that 144 is the
house number!