### 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!

Can you predict where $29^2$ will appear? Or $34^2$? Or $52^2$?
By representing an odd number as $2n+1$, can you explain any of the patterns in the odd square numbers?