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?

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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?

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How many ways can Mathias solve this symmetry challenge?

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

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Weekly Problem 35 - 2012

How many more triangles need to be shaded to make the pattern have a line of symmetry?

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Weekly Problem 31 - 2014

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

Challenge Level

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

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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?

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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?

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A card with the letter N on it is rotated through two different axes. What does the card look like at the end?

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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?

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Weekly Problem 11 - 2011

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

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

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

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

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Given how much this 50 m rope weighs, can you find how much a 100 m rope weighs, if the thickness is different?

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

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What are the possible perimeters of the larger triangle?

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

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

Challenge Level

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