This is part of our collection of Short Problems.
You may also be interested in our longer problems on Construction.
Printable worksheets containing selections of these problems are available here.
problem
Folded A4
Age
11 to 14
Challenge level
What shapes can be made by folding an A4 sheet of paper only once?
problem
Defined distances
Age
11 to 14
Challenge level
Mark writes four points on a line at different lengths. What is the distance between the two points furthest apart?
problem
Contact circles
Age
14 to 16
Challenge level
These four touching circles have another circle hiding amongst them...
problem
Either side
Age
14 to 16
Challenge level
A disc with a pencil inside it is rolled around the outside and inside of a wire equilateral triangle. What shape is drawn by the pencil?
problem
Pink and white
Age
14 to 16
Challenge level
The white square slides once around the pink square. Through what distance does the point P on the white square move?
problem
Snail's pace
Age
14 to 16
Challenge level
A snail is at the corner of a cube. What proportion of the cube's surface can the snail reach within an hour?
problem
Triangular wheel
Age
14 to 16
Challenge level
An equilateral triangle is rolled along a line. What is the length of the path traced out by one of its vertices?
problem
3-sided
Age
14 to 16
Challenge level
How many triangles can Jack draw with two sides of lengths $6$cm and $8$cm and an area of $7$cm$^2$?