A spreadsheet is a good tool for this puzzle.
Can you explain this phenomenon?
Look only at the last three digits of 2i, with i=1,2,3,...
Eventually the series starts to repeat earlier values.
At what value of i does it repeat, and how long is the cycle?
- Do the same for the last three digits of ki, (2 < k < 20).
- Do the same for the last N digits of ki, (1 < N < 5).
Source: Original. Based upon a puzzle from reader Jimmy Chng Gim Hong.
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