Visualising and representing

problem

Redblue

Age

7 to 11

Challenge level

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
problem

Shunting Puzzle

Age

7 to 11

Challenge level

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
problem

Single Track

Age

7 to 11

Challenge level

What is the best way to shunt these carriages so that each train can continue its journey?
problem

Waiting for Blast Off

Age

7 to 11

Challenge level

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
problem

Counters

Age

7 to 11

Challenge level

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
problem

Cuboid-In-A-Box

Age

7 to 11

Challenge level

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
problem

Peg Rotation

Age

7 to 11

Challenge level

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?
problem

Cube Drilling

Age

7 to 11

Challenge level

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
problem

More Pebbles

Age

7 to 11

Challenge level

Have a go at this 3D extension to the Pebbles problem.
problem

Drilling Many Cubes

Age

7 to 14

Challenge level

A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.