Exploring and noticing

problem
A mean tetrahedron

Age

11 to 14

Challenge level

Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?
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
Number sandwiches

Age

7 to 14

Challenge level

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
problem
Two ladders

Age

14 to 16

Challenge level

Two ladders are propped up against facing walls. At what height do the ladders cross?
problem
Triangle midpoints

Age

14 to 16

Challenge level

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
problem
Pair sums

Age

11 to 14

Challenge level

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
problem
Have you got it?

Age

11 to 14

Challenge level

Can you explain the strategy for winning this game with any target?
problem
Days and dates

Age

11 to 14

Challenge level

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
problem
Birthday cakes

Age

5 to 7

Challenge level

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?
problem
Domino join up

Age

5 to 7

Challenge level

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?