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

### 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?

Peri the winkle starts at the origin and slithers around some semicircles. Where does she end her expedition?

problem

### Symmetriangle

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

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

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

Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?

problem

### Reflected Back

Imagine reflecting the letter P in all three sides of a triangle in turn. What is the final result?

problem

### 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?

problem

### 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?

problem

### 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?

problem

### 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?

problem

### Kangaroo Hops

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

How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?

problem

### Growing Triangle

If the base and height of a triangle are increased by different percentages, what happens to its area?

problem

### 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?

problem

### 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?

problem

### Half Area

The horizontal red line divides this equilateral triangle into two shapes of equal area. How long is the red line?