Problems
Three by Three
Stage: 1 Challenge Level: 
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
The Amazing Splitting Plant
Stage: 1 Challenge Level:
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Cat Food
Stage: 2 Challenge Level:
Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?
Seating Arrangements
Stage: 2 Challenge Level:
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Clever Keys
Stage: 2 Short Challenge Level:
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
Making Triangles
Stage: 2 Challenge Level:
Draw in two straight lines to form a total of eight triangles.
Arranging the Tables
Stage: 2 Challenge Level:
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
World of Tan - Granma T
Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of Granma T?
Sometimes We Lose Things
Stage: 2 Challenge Level:
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
Pouring the Punch Drink
Stage: 2 Challenge Level:
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
Like Powers
Stage: 3 Challenge Level:
Investigate 1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n and 2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n for different values of n.
Thirty Six Exactly
Stage: 3 Challenge Level:
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Three Four Five
Stage: 4 Challenge Level:
Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.
Rachel's Problem
Stage: 4 Challenge Level:
Is it true that 99^n has 2n digits and 999^n has 3n digits? Investigate!
Logosquares
Stage: 5 Challenge Level:
Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.
Absurdity Again
Stage: 5 Challenge Level:
What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?
Thasan's Flight
Stage: 5 Challenge Level:
An aircraft flies on a bearing of 070 degrees at 350 km/hour with wind blowing at 40 km/hour from 340 degrees. Find the actual speed and bearing of the aircraft.
Old Nuts
Stage: 5 Challenge Level:
In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?
Lunar Leaper
Stage: 5 Challenge Level:
Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?
