### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

# Medal Ceremony

##### Stage: 3 and 4 Short Challenge Level:

There are $6$ different students who could receive the first gold medal, then $5$ others for the second and $4$ remaining for the third. Therefore there are $6 \times 5 \times 4 = 120$ orders in which the medals can be presented. However, this counts each set of three people winning the medals in each of the six orders, so there are $120 \div 6 = 20$ sets of three people who could win gold.

For each of these, one of the remaining three people must win bronze and the others silver, so there are $20 \times 3 = 60$ ways in which the medals can be awarded.

This problem is taken from the UKMT Mathematical Challenges.