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 Yeow of Riccarton High School, Christchruch, New Zealand. Other correct solutions were received from Andrei Lazanu (School 205, Bucharest), Mary Fortune (Birchwood Community High School), Rachel Willis and Sebastian Crane (Hethersett High School) and Claire Gurney.

Well first, I found all three digit numbers which are square numbers...
10² = 100
11² = 121
12² = 144
13² = 169
14² = 196
15² = 225
16² = 256
17² = 289
18² = 324
19² = 361
20² = 400
21² = 441
22² = 484
23² = 529
24² = 576
25² = 625
26² = 676
27² = 729
28² = 784
29² = 841
30² = 900
31² = 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!