Transformations - Short Problems


This is part of our collection of Short Problems.

You may also be interested in our longer problems on Transformations.

Semaphore

Age 11 to 14 Short Challenge Level:

Weekly Problem 34 - 2009
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

Age 11 to 14 Short Challenge Level:

Weekly Problem 24 - 2016
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?

Grid Without Lines

Age 11 to 14 Short Challenge Level:

Weekly Problem 40 - 2010
Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?

Symmetriangle

Age 11 to 14 Short Challenge Level:

Weekly Problem 35 - 2012
How many more triangles need to be shaded to make the pattern have a line of symmetry?

Turning N Over

Age 11 to 14 Short Challenge Level:

Weekly Problem 34 - 2013
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

Age 11 to 14 Short Challenge Level:

Weekly Problem 24 - 2011
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?

Flag-tastic

Age 11 to 14 Short Challenge Level:

How many different flags can you make?

Peri the Winkle

Age 11 to 14 Short Challenge Level:

Weekly Problem 31 - 2014
Peri the winkle starts at the origin and slithers around some semicircles. Where does she end her expedition?

Flagged Up

Age 11 to 14 Short 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?

Reflected Back

Age 11 to 14 Short Challenge Level:

Weekly Problem 18 - 2015
Beatrix relfects the letter P in all three sides of a triangle in turn. What is the final result?

Potatoes

Age 11 to 14 Short 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?

Back in Time

Age 11 to 14 Short Challenge Level:

Weekly Problem 29 - 2015
How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?

Grid Symmetry

Age 11 to 14 Short Challenge Level:

How many ways can Mathias solve this symmetry challenge?

Kangaroo Hops

Age 11 to 14 Short Challenge Level:

Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?

Similar Perimeter

Age 14 to 16 Short Challenge Level:

What is the smallest possible perimeter of the larger triangle described?

Pendants

Age 14 to 16 Short Challenge Level:

What proportion of each of these pendants will be made of gold?

Photocopied Map

Age 14 to 16 Short Challenge Level:

What will the scale on this map be after it has been photocopied?

Climbing Ropes

Age 14 to 16 Short 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?

Growing Triangle

Age 14 to 16 Short Challenge Level:

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

Half Area

Age 14 to 16 Short Challenge Level:

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

Rotation and Area

Age 14 to 16 Short Challenge Level:

Point A is rotated to point B. Can you find the area of the triangle that these points make with the origin?

Coloured Black

Age 14 to 16 Short Challenge Level:

An ink stamp draws out a shape when it is rotated. What is its area?