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lamp algorithm


Best Answer plasmid, 29 April 2014 - 03:31 PM

Possibly solved, but not completely proven.

Spoiler for number of lamps that can have a single lamp toggled with an M 105 tool

Spoiler for turning off lamps with an M 32 tool

Spoiler for putting that all together
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4 replies to this topic

#1 BMAD

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Posted 15 April 2014 - 05:47 AM


N lamps are set in a circle, and for each integer M you have a tool that can toggle the state (on/off) of any set of M consecutive lamps.
Find a possible N which satisfies the following statements:
The sum of its digits is less than 10.
By applying the tool for M=105 several times, we can toggle a single lamp.
If we remove one lamp and start from a random initial setting for the remaining N-1 lamps, the probability that there exists a way to apply the tool for M=32 several times and switch all the lamps off is positive and less than 0.0011%.
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#2 Rob_G

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Posted 15 April 2014 - 05:14 PM

Spoiler for Question


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#3 BMAD

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Posted 22 April 2014 - 02:41 PM

no.


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#4 plasmid

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Posted 28 April 2014 - 06:17 AM

This is a tough problem. At least for me. This is what I've got right now.
Spoiler for

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#5 plasmid

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Posted 29 April 2014 - 03:31 PM   Best Answer

Possibly solved, but not completely proven.
Spoiler for number of lamps that can have a single lamp toggled with an M 105 tool

Spoiler for turning off lamps with an M 32 tool

Spoiler for putting that all together

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