Compare squares and cubes, search integer pairs, and test a misleading near miss.
Colour neighbouring regions and explore why four colours are enough for a planar map.
Compare square stacks with close-packed layers of equal spheres.
Find prime pairs for an even number and compare examples with a universal claim.
Trace the exact 3n + 1 journey of a positive integer.
Build a Koch snowflake or Sierpiński triangle one stage at a time.
Move guests to make room in a hotel with infinitely many occupied rooms.
Compare a number grid and an Ulam spiral, then investigate the highlighted primes.
Rotate a band and trace its boundary to explore a surface with one side.
Remove middle thirds and discover why zero length does not mean no points.
Wrap numbers around a clock and investigate when division has an inverse.
Compare two nearby starting values under the same simple rule.
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