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0scar · 2020-07-30, 05:33

A friend of mine suggested a nice "spin-off" puzzle.

If you solved July 2020 main problem by using three letters or more,
and your dictionary includes letters "I", "B", and "M",
then how many times does substring "IBM" appear in your solution?

Let IBM(n) be the number of occurrences within n-th string of your solution.
Does this sequence follow some nice pattern?

A trivial upper bound is IBM(n) <= LENGTH(n)/3 = FIBONACCI(n)*FIBONACCI(n+1)/3.
A slightly sharper bound is given by RARE(n), the minimum among the occurrences of letters "I", "B", and "M".

What about your ratio IBM(n) / LENGTH(n)?
What about your ratio IBM(n) / RARE(n)?

2020-07-30, 05:33	#4
0scar Jan 2020 30₁₀ Posts	Spin-off A friend of mine suggested a nice "spin-off" puzzle. If you solved July 2020 main problem by using three letters or more, and your dictionary includes letters "I", "B", and "M", then how many times does substring "IBM" appear in your solution? Let IBM(n) be the number of occurrences within n-th string of your solution. Does this sequence follow some nice pattern? A trivial upper bound is IBM(n) <= LENGTH(n)/3 = FIBONACCI(n)*FIBONACCI(n+1)/3. A slightly sharper bound is given by RARE(n), the minimum among the occurrences of letters "I", "B", and "M". What about your ratio IBM(n) / LENGTH(n)? What about your ratio IBM(n) / RARE(n)?