game
Khun phaen escapes to freedom
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Visualising and representing
problem
Matchsticks
Age
7 to 11
Challenge level
Reasoning about the number of matches needed to build squares that
share their sides.
problem
Just rolling round
Age
14 to 16
Challenge level
P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
of P?
problem
Instant insanity
Age
11 to 18
Challenge level
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
problem
Hallway borders
Age
11 to 14
Challenge level
What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?
problem
How many dice?
Age
11 to 14
Challenge level
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find there are 2 and only 2 different standard dice. Can you prove this ?
problem
Take ten
Age
11 to 14
Challenge level
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
problem
Six to four
Age
5 to 7
Challenge level
Move four sticks so there are exactly four triangles.
problem
Logo challenge - triangles-squares-stars
Age
11 to 16
Challenge level
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
problem
Corridors
Age
14 to 16
Challenge level
A 10x10x10 cube is made from 27 2x2 cubes with corridors between
them. Find the shortest route from one corner to the opposite
corner.