Cycles and Time: Repeating Patterns

Methods in this video

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1. 1

   Where? Drop the full cycles, use the remainder

   ▶ 0:45

   When to use it: A pattern, grid position, turn or pass keeps repeating, and the question asks what or where a far-off item is, or where something ends up after many moves. The cycle is not a week.

   • Count one full cycle first: count the actual tiles, cells or moves, not the number of colours.
   • Divide the position by the cycle length and ignore the quotient: remainder r means the r-th item in the cycle, and no remainder means the last item. For moves, no remainder means back at the start.
   • Drop full cycles in each direction, then cancel. If only one coordinate cycles, work out the other one separately.