Transformations - Short Problems
Peri the Winkle
Weekly Problem 31 - 2014
Peri the winkle starts at the origin and slithers around some semicircles. Where does she end her expedition?
Flagged Up
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?
Potatoes
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?
Grid Symmetry
How many ways can Mathias solve this symmetry challenge?
Grid Without Lines
Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?
Symmetriangle
Weekly Problem 35 - 2012
How many more triangles need to be shaded to make the pattern have a line of symmetry?
Turning N Over
A card with the letter N on it is rotated through two different axes. What does the card look like at the end?
Reading from Behind
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?
Reflected Back
Imagine reflecting the letter P in all three sides of a triangle in turn. What is the final result?
Semaphore
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?
Doubly Symmetric
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?
Kangaroo Hops
Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?
Climbing Ropes
Given how much this 50 m rope weighs, can you find how much a 100 m rope weighs, if the thickness is different?
Growing Triangle
If the base and height of a triangle are increased by different percentages, what happens to its area?
Similar Perimeter
What are the possible perimeters of the larger triangle?
Pendants
What proportion of each of these pendants will be made of gold?
Rotation and Area
Point A is rotated to point B. Can you find the area of the triangle that these points make with the origin?
Back in Time
How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?
Photocopied Map
What will the scale on this map be after it has been photocopied?
Half Area
The horizontal red line divides this equilateral triangle into two shapes of equal area. How long is the red line?
Coloured Black
An ink stamp draws out a shape when it is rotated. What is its area?
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Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
