Square numbers

problem
Smith and Jones

Age

14 to 16

Challenge level

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
problem
Pythagorean quadruple

Age

14 to 16

Challenge level

The sum of three square numbers equals $121$. What can those numbers be...
problem
Time of birth

Age

11 to 14

Challenge level

A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. When was she born?
problem
Digat

Age

11 to 14

Challenge level

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
problem
Triangular triples

Age

14 to 16

Challenge level

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
problem
Triangles within squares

Age

14 to 16

Challenge level

Can you find a rule which relates triangular numbers to square numbers?
problem
Relative powers

Age

14 to 16

Challenge level

The square of a number is 12 more than the number itself. The cube of the number is 9 times the number. What is the number?
problem
Square sum

Age

14 to 16

Challenge level

One of these numbers is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?
problem
No square sums

Age

14 to 16

Challenge level

How many numbers do you need to remove to avoid making a perfect square?
problem
Square triangle

Age

11 to 14

Challenge level

How many triangles have all three angles perfect squares (in degrees)?