Try these unsolved problems
Clock Face
Stage:2 Challenge Level:
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Putting Two and Two Together
Stage:2 Challenge Level:
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
Locate the Lion's Lair
Stage:2 Challenge Level:
Use the sightings of the lion to guess the location of its lair.
How Random!
Stage:2 Challenge Level:
Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?
Largest Product
Stage:3 Challenge Level:
Which set of numbers that add to 10 have the largest product?
In the Bag
Stage:3 Challenge Level:
Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?
Playing Connect Three
Stage:3 Challenge Level:
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
Conway's Chequerboard Army
Stage:3 Challenge Level:
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Where Is the Dot?
Stage:3 Challenge Level:
A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?
Cops and Robbers
Stage:2 and 3 Challenge Level:
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
First Connect Three
Stage:2 and 3 Challenge Level:
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Circumspection
Stage:4 Challenge Level:
M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.
A Scale for the Solar System
Stage:4 Challenge Level:
The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?
The Perforated Cube
Stage:4 Challenge Level:
A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?
Exhaustion
Stage:4 Challenge Level:
Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
Distribution Differences
Stage:4 Challenge Level:
How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?
Tri-split
Stage:4 Challenge Level:
A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?
Giant Holly Leaf
Stage:4 Challenge Level:
Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).
Modular Knights
Stage:5 Challenge Level:
Try to move the knight to visit each square once and return to the starting point. Move either 2 steps one way and one perpendicular (as in chess) or generalise to a steps one way and b the other.
More Bridge Building
Stage:5 Challenge Level:
Which parts of these framework bridges are in tension and which parts are in compression?
Scale Invariance
Stage:5 Challenge Level:
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Spot the Difference
Stage:5 Short Challenge Level:
If you plot these graphs they may look the same, but are they?
Circular Circuitry
Stage:5 Challenge Level:
What will happen when you switch on these circular circuits?
Random Inequalities
Stage:5 Challenge Level:
Can you build a distribution with the maximum theoretical spread?
Harmonically
Stage:5 Challenge Level:
Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?
Pattern Recognition
Stage:5 Challenge Level:
When does a pattern start to exhibit structure? Can you crack the code used by the computer?
Impossible Triangles?
Stage:4 and 5 Challenge Level:
Which of these triangular jigsaws are impossible to finish?
Lion Hunting
Stage:4 and 5 Challenge Level:
A killer lion is causing devastation. From the locations of its reported activity, can you work out where its lair is located?
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