### 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?

# Truncated Tetrahedron

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

At each vertex, the piece that has been removed is a regular tetrahedron. Three of the edges of this are the pieces of edge that are lost from the original tetrahedron, the other three are the new edges of the truncated tetrahedron. Since all the edges are the same length, this means the total length of the edges remains unchanged.

Therefore, the total length of the edges is $6\text{cm} \times 6 = 36\text{cm}$.

This problem is taken from the UKMT Mathematical Challenges.
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