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?
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...
...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!