Problems
Writing Digits
Stage: 1 Short Challenge Level: 
Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?
Up and Down
Stage: 1 Challenge Level:
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
Magic Squares 3x3
Stage: 1 Challenge Level:
Fill in the numbers to make the sum of each row, column and diagonal equal to 15.
Magic Squares 4x4
Stage: 2 Challenge Level:
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
World of Tan - Little Ming
Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of Little Ming?
Team Scream
Stage: 2 Challenge Level:
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
Grrrrrrrrrrrreat Squares
Stage: 2 and 3 Challenge Level:
Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
Man Food
Stage: 2 and 3 Challenge Level:
Sam displays cans in 3 triangular stacks. With the same number he could make one large triangular stack or stack them all in a square based pyramid. How many cans are there how were they arranged?
Icosagram
Stage: 3 Challenge Level:
Draw a pentagon with all the diagonals. This is called a pentagram. How many diagonals are there? How many diagonals are there in a hexagram, heptagram, ... Does any pattern occur when looking at. . . .
The Pi Are Square
Stage: 3 Challenge Level:
A circle with the radius of 2.2 centimetres is drawn touching the sides of a square. What area of the square is NOT covered by the circle?
Lying and Cheating
Stage: 3 Challenge Level:
Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!
Sum Equals Product
Stage: 3 Challenge Level:
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . .
Inclusion Exclusion
Stage: 3 Challenge Level:
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
LOGO Challenge 5 - Patch
Stage: 3 and 4 Challenge Level:
Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?
Ladder and Cube
Stage: 4 Challenge Level:
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
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?
Some Cubes
Stage: 5 Challenge Level:
The sum of the cubes of two numbers is 7163. What are these numbers?
Just Touching
Stage: 5 Challenge Level:
Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?
Elsewhere...
Featured Solutions
Articles & Games
Learning Mathematics Through Games Series: 1. Why Games?
This article supplies teachers with information that may be useful in better understanding the nature of games and their role in teaching and learning mathematics.
