Exploding Dots

The 1 3 1 \leftarrow3 machine:

  • The dots initially go into the right most box.
  • Whenever there are three (or more) dots are in the same box, then three dots will explode and become one dot on box to the left, unless there is no box one place to the left.

How many dots do we have to place to obtain the code 1 0 2 0 \boxed{1} \boxed{0}\boxed{2}\boxed{0} ?


The answer is 33.

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1 solution

Peter Michael
Aug 5, 2017

The powers of three

Twenty seven and two threes

Which makes thirty-three

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