Problems
Excel Interactive Resource: Remainder
Stage: Challenge Level: 
Use an interactive Excel spreadsheet to investigate remainders.
Excel Interactive Resource: X Marks the Spot
Stage: Challenge Level:
Use Excel to investigate multiplication and number.
1, 2, 3 Magic Square
Stage: 2 Challenge Level:
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Seven Pots of Plants
Stage: 2 Challenge Level:
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
A Square Deal
Stage: 2 Challenge Level:
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
Triangle Island
Stage: 2 Challenge Level:
You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?
Symmetry Challenge
Stage: 2 Challenge Level:
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
Counters
Stage: 2 Challenge Level:
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Make 37
Stage: 2 and 3 Challenge Level:
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Pick's Theorem
Stage: 3 Challenge Level:
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Isometrically
Stage: 3 Challenge Level:
How many unique symmetrical shapes can you make by shading four small triangles?
Konigsberg
Stage: 3 Challenge Level:
Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
Cinema Problem
Stage: 3 Challenge Level:
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Top-heavy Pyramids
Stage: 3 Challenge Level:
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
Take Three from Five
Stage: 3 Challenge Level:
Can you guarantee that from any group of 5 numbers it is always possible to choose three numbers that will add up to a multiple of 3?
LOGO Challenge - the Logic of LOGO
Stage: 3 and 4 Challenge Level:
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
Postage
Stage: 4 Challenge Level:
The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .
Power Quady
Stage: 4 Challenge Level:
Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.
Counting Binary Ops
Stage: 4 Challenge Level:
How many ways can the terms in an ordered list be combined by repeating a single binary operation. Show that for 4 terms there are 5 cases and find the number of cases for 5 terms and 6 terms.
Magic W Wrap Up
Stage: 5 Challenge Level:
Prove that you cannot form a Magic W with a total of 12 or less or with a with a total of 18 or more.
