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A Square and A Cube

Which count is the job asking for

A courtyard, an open floor, needs tiling. A roof tank needs filling. Both are 4 units along a side.

A flat patch, 4 tiles across: 16.
Step 1 of 3
  1. A flat patch, 4 tiles across: 16.
  2. A filled space, 4 blocks deep too: 64.
  3. Same side, two different counts.

Rule: Covering a square patch wants side times side. Filling a cube-shaped space wants side times side times side.

  • Tiles on a square floor cover a square patch.
  • A cube-shaped tank or crate is a space to fill.

Watch out!

The word "square" in a job does not decide. A box of square barfi is being filled, not covered. So count in three directions: across, deep and high.

Pick a job. Slide its side. Switch to the count it needs.

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This track

  1. 0 Start here
  2. 1 A number you can draw as a square
  3. 2 Each new layer is the next odd number
  4. 3 A test that can only say no
  5. 4 Going back to the side you started from
  6. 5 Pairing the primes finds the side
  7. 6 Checkpoint: squares, the staircase and roots
  8. 7 When no whole number fits
  9. 8 A cube number counts real cubes
  10. 9 What cubes end in, and what they add up to
  11. 10 Grouping the primes in threes
  12. 11 Which count is the job asking for
  13. 12 Checkpoint: in between, cubes and cube roots
  14. 13 The big picture
  15. 14 Track quiz

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