Problems
Red Express Train
Stage: 1 Challenge Level: 
The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
Whose Sandwich?
Stage: 1 Challenge Level:
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
Cutting Corners
Stage: 2 Challenge Level:
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Pathways
Stage: 2 Short Challenge Level:
A garden has square flower beds surrounded by paths. Can you find a way to walk all around the paths without walking on the same part twice?
Domino Square
Stage: 2 Challenge Level:
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
Prison Cells
Stage: 2 Challenge Level:
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Reza's Age
Stage: 3 Challenge Level:
In three years time Reza's age will be the square of his age of three years ago. How old is he? Find similar relationships for differences other than 3 years.
Not So Little X
Stage: 3 Challenge Level:
Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?
Long Multiplication
Stage: 3 Challenge Level:
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
Multiplication Magic
Stage: 4 Challenge Level:
Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .
Hand Swap
Stage: 4 Challenge Level:
My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .
Round and Round
Stage: 4 Challenge Level:
Prove that the shaded area of the semicircle is equal to the area of the inner circle.
Shades of Fermat's Last Theorem
Stage: 5 Challenge Level:
The familiar Pythagorean 3-4-5 triple gives one solution to (x-1)^n + x^n = (x+1)^n so what about other solutions for x an integer and n= 2, 3, 4 or 5?
Mean Geometrically
Stage: 5 Challenge Level:
A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?
Fixing It
Stage: 5 Challenge Level:
A and B are fixed points on a circle and PQ is a variable diameter. Make and prove a conjecture about the locus of the intersection of AQ and BP.
