### Triangular Triples

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

### Smith and Jones

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!

# Triangles Within Squares

##### Age 14 to 16 Challenge Level:

Well explained by Tom, from Cottenham Village College

The answer I got for $T_n$ is: $8T_n+1=(2n+1)^2$

The $2n+1$ part is because the diagram looks like this for $T_3$
$2T_n$ form a rectangle $n$ by $n+1$

The four rectangles rotate around the centre and together make a square of side $n+(n+1)$

So we get the equation $8T_n+1=(2n+1)^2$