Problems
Cubes Cut Into Four Pieces
Stage: 1 Challenge Level: 
Eight children each had a cube made from modelling clay. They cut them into 4 pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?
A Puzzling Cube
Stage: 2 Challenge Level:
Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?
Square Corners
Stage: 2 Challenge Level:
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Inside Seven Squares
Stage: 2 Challenge Level:
What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
The Third Dimension
Stage: 2 Challenge Level:
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
All Square
Stage: 3 Challenge Level:
The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
LOGO Challenge - Triangles
Stage: 3 Challenge Level:
The theme in the rest of the magazine is TRIANGLES. But triangles are available in all sizes and in 'several' varieties. Similarly this month LOGOland will focus on triangles - equilateral triangles. . . .
Triangular Tantaliser
Stage: 3 Challenge Level:
Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.
Covering Cups
Stage: 3 Challenge Level:
What is the shape and dimensions of a box that will contain six cups and have as small a surface area as possible.
Sums of Pairs
Stage: 3 and 4 Challenge Level:
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
Tilting Triangles
Stage: 4 Challenge Level:
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
Crescents and Triangles
Stage: 4 Challenge Level:
Triangle ABC is right angled at A and semi circles are drawn on all three sides producing two 'crescents'. Show that the sum of the areas of the two crescents equals the area of triangle ABC.
Tetra Inequalities
Stage: 5 Challenge Level:
Prove that in every tetrahedron there is a vertex such that the three edges meeting there have lengths which could be the sides of a triangle.
Polite Numbers
Stage: 5 Challenge Level:
A polite number can be written as the sum of two or more consecutive positive integers. Find the consecutive sums giving the polite numbers 544 and 424. What characterizes impolite numbers?
Instant Insanity
Stage: 5 Challenge Level:
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
