August 2003, Stage 3&4

Problems

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?

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?

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.

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?

Stringing it Out

Age 14 to 16 Challenge Level:

Explore the transformations and comment on what you find.

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.