This is part of our collection of Short Problems.
You may also be interested in our longer problems on Transformations.
Printable worksheets containing selections of these problems are available here.
problem
Symmetriangle
Age
11 to 14
Challenge level
Weekly Problem 35 - 2012
How many more triangles need to be shaded to make the pattern have a line of symmetry?
How many more triangles need to be shaded to make the pattern have a line of symmetry?
problem
Flagged up
Age
11 to 14
Challenge level
Weekly Problem 31 - 2008
The flag is given a half turn anticlockwise about the point O and is then reflected in the dotted line. What is the final position of the flag?
The flag is given a half turn anticlockwise about the point O and is then reflected in the dotted line. What is the final position of the flag?
problem
Potatoes
Age
11 to 14
Challenge level
Weekly Problem 19 - 2009
When I looked at the greengrocer's window I saw a sign. When I went in and looked from the other side, what did I see?
When I looked at the greengrocer's window I saw a sign. When I went in and looked from the other side, what did I see?
problem
Grid without lines
Age
11 to 14
Challenge level
Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?
problem
Peri the winkle
Age
11 to 14
Challenge level
Weekly Problem 31 - 2014
Peri the winkle starts at the origin and slithers around some semicircles. Where does she end her expedition?
Peri the winkle starts at the origin and slithers around some semicircles. Where does she end her expedition?
problem
Grid symmetry
Age
11 to 14
Challenge level
How many ways can Mathias solve this symmetry challenge?
problem
Turning N over
Age
11 to 14
Challenge level
A card with the letter N on it is rotated through two different axes. What does the card look like at the end?
problem
Semaphore
Age
11 to 14
Challenge level
I am standing behind five pupils who are signalling a five-digit number to someone on the opposite side of the playground. What number is actually being signalled?
problem
Reading from behind
Age
11 to 14
Challenge level
Can you find the time between 3 o'clock and 10 o'clock when my digital clock looks the same from both the front and back?
problem
Reflected back
Age
11 to 14
Challenge level
Imagine reflecting the letter P in all three sides of a triangle in turn. What is the final result?
problem
Doubly symmetric
Age
11 to 14
Challenge level
What is the smallest number of additional squares that must be shaded so that this figure has at least one line of symmetry and rotational symmetry of order 2?
problem
Kangaroo hops
Age
11 to 14
Challenge level
Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?
Kanga hops ten times in one of four directions. At how many different points can he end up?
problem
Back in time
Age
14 to 16
Challenge level
How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?
problem
Growing triangle
Age
14 to 16
Challenge level
If the base and height of a triangle are increased by different percentages, what happens to its area?
problem
Pendants
Age
14 to 16
Challenge level
What proportion of each of these pendants will be made of gold?
problem
Rotation and area
Age
14 to 16
Challenge level
Point A is rotated to point B. Can you find the area of the triangle that these points make with the origin?
problem
Photocopied map
Age
14 to 16
Challenge level
What will the scale on this map be after it has been photocopied?
problem
Climbing ropes
Age
14 to 16
Challenge level
Given how much this 50 m rope weighs, can you find how much a 100 m rope weighs, if the thickness is different?
problem
Similar perimeter
Age
14 to 16
Challenge level
What are the possible perimeters of the larger triangle?
problem
Coloured black
Age
14 to 16
Challenge level
An ink stamp draws out a shape when it is rotated. What is its area?
problem
Half area
Age
14 to 16
Challenge level
The horizontal red line divides this equilateral triangle into two shapes of equal area. How long is the red line?