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Construct-o-straws

Make a cube out of straws and have a go at this practical challenge.

Matchsticks

Reasoning about the number of matches needed to build squares that share their sides.

Little Boxes

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Knight's Swap

Age 7 to 11
Challenge Level

Several people decided that 16 moves were needed to swap the stars and moons. The really interesting part is the ways they invented to tell us what the moves were ...
Joshua (Brooklands Primary School, Suffolk) numbered the squares 1 to 9 like this:

Solution

He says, "I could do the swap of the moons and stars in 16 moves:

  1. star at 7 goes to 6
  2. moon at 1 goes to 8
  3. star at 6 goes to 1
  4. moon at 3 goes to 4
  5. star at 9 goes to 2
  6. moon at 4 goes to 9
  7. moon at 8 goes to 3
  8. star at 2 goes to 7
  1. moon at 3 goes to 4
  2. moon at 9 goes to 2
  3. moon at 4 goes to 9
  4. star at 7 goes to 6
  5. moon at 2 goes to 7
  6. star at 1 goes to 8
  7. star at 6 goes to 1
  8. star at 8 goes to 3"

Thomas (Tattingstone School, UK) used the game-board like a map grid.

Thomas's solution.

  • Star 1 to B3
  • Star 2 to A2
  • Moon 1 to B1
  • Moon 2 to C2
  • Star 1 to C1
  • Star 2 to C3
  • Moon 1 to A3
  • Moon 2 to A1
  • Star 1 to A2
  • Star 2 to B1
  • Moon 1 to C2
  • Moon 2 to B3
  • Star 1 to C3
  • Star 2 to A3
  • Moon 1 to A1
  • Moon 2 to C1

Jaimee (Tattingstone School, UK) gave each square a letter and called the Stars S1 and S2, and the Moons M1 and M2.

Jaimee's solution.

  • M1 to F
  • S1 to B
  • M1 to G
  • S2 to D
  • M2 to H
  • S2 to C
  • M2 to A
  • M2 to F
  • S1 to I
  • M1 to B
  • M2 to G
  • S1 to D
  • M1 to I
  • S2 to H
  • S2 to A
  • S1 to C

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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