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Special 24

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

A Right Charlie

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

A Right Charlie

Charlie's house number is a three-digit square number.

This number when reversed is also a square and is Charlie's telephone extension at work.

His car registration number is  a four-digit square number and is formed from his house number by repeating the right hand digit.

What is Charlie's house number?

Why do this problem?

This problem requires systematic working and will increase children's familiarity with square numbers.

Key questions

What three-digit square numbers do you know?
How do you know you haven't missed out any three-digit square numbers?

Possible extension

Some pupils may enjoy the challenge of Gran, How Old Are You? which is a similar numerical problem.

Possible support

Many children will find the use of a calculator invaluable for this problem.