### Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

If you had 36 cubes, what different cuboids could you make?

# Family Tree

##### Stage: 2 Challenge Level:

You have to use the clues given in the question to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not. This question does not require any mathematical knowledge but it does call for logical thinking which is needed to do mathematics.

In the family tree square boxes indicate males and round boxes females.

Each set of siblings (brothers and sisters) is in descending order of age from left to right across the page.

Exactly five of the people represented in the tree are mathematicians.

Unusually for this sort of problem, everyone always tells the truth.

Last Christmas they were assembled together (and only people on this family tree were there). They made the following statements and, of course, none of them would be so rude as to mention anyone who was not present.

It may help you to know that E is the youngest male in the family, and that he and K are both mathematicians.

 A. My father is a mathematician. B. So is mine. C. And mine. D. And mine. E. Mine too. F. Neither of my parents is a mathematician but my one and only brother is. G. Only one of us females is a mathematician but it's not me. H. I've given birth to two mathematicians, no more and no less. I. I am the oldest mathematician in the family. J. My brother-in-law is a mathematician. C. My husband isn't. D. Exactly one of my cousins is. G. B is my granddaughter.