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?

Draught Plans

Stage: 3 and 4 Short Challenge Level:

There are four rows and four columns, so we need eight different sums. The smallest eight sums (if possible) would be $0, 1, 2, 3, ... , 7$. Since each draughts is counted towards the sum of a row and the sum of a column, we would need $\frac{1}{2}(0+1+2+ ...+7) = 14$ draughts. The diagram shows it is possible to place $14$ draughts on the board to create the eight smallest sums (the numbers in the cells represent how many draughts there are in each cell, and the column and row totals are shown).

Example 1:

Example 2:

This problem is taken from the UKMT Mathematical Challenges.