Problems
4 Dom
Stage: 1 Challenge Level: 
Use these four dominoes to make a square that has the same number of dots on each side.
Flashing Lights
Stage: 2 Challenge Level:
Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?
Fake Gold
Stage: 2 Challenge Level:
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
Bean Bags for Bernard's Bag
Stage: 2 Challenge Level:
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
Forgot the Numbers
Stage: 2 Challenge Level:
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
World of Tan - the Past, Present and Future
Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of the telescope and microscope?
Professional Circles
Stage: 2 Challenge Level:
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
ABC
Stage: 2 Challenge Level:
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
AP Rectangles
Stage: 3 Challenge Level:
An AP rectangle is one whose area is numerically equal to its perimeter. If you are given the length of a side can you always find an AP rectangle with one side the given length?
Add 3 Dice
Stage: 3 Challenge Level:
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to. . . .
LOGO Challenge 6 - Triangles and Stars
Stage: 3 and 4 Challenge Level:
Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.
Picture Story
Stage: 4 Challenge Level:
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
Proximity
Stage: 4 Challenge Level:
We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
Exhaustion
Stage: 4 Challenge Level:
Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
Walkabout
Stage: 4 Challenge Level:
A walk is made up of diagonal steps from left to right, starting at the origin and ending on the x-axis. How many paths are there for 4 steps, for 6 steps, for 8 steps?
Angle Trisection
Stage: 4 Challenge Level:
It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
Knock-out
Stage: 5 Challenge Level:
Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?
Climbing Powers
Stage: 5 Challenge Level:
2^3^4 could be (2^3)^4 or 2^(3^4). Does it make any difference? For both definitions, which is bigger r^r^r^r... where the powers of r go on for ever, or (r^r)^r, where r is the square root of 2?
Five Circuits, Seven Spins
Stage: 5 Challenge Level:
A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.
