August 2003, Stage 3&4

Problems

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Reflecting Squarely

Age 11 to 14 Challenge Level:

In how many ways can you fit all three pieces together to make shapes with line symmetry?

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Threesomes

Age 11 to 14 Challenge Level:

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

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Bow Tie

Age 11 to 14 Challenge Level:

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

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Just Repeat

Age 11 to 14 Challenge Level:

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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Stringing it Out

Age 14 to 16 Challenge Level:

Explore the transformations and comment on what you find.

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Old Versions of NRICH Problems

Age 11 to 18 Challenge Level:

Original text of NRICH problems, as featured in Charlie and Alison's BCME session 2018.