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dice problem


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12 replies to this topic

#1 phil1882

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Posted 24 August 2013 - 02:53 AM

you want to throw three 8 sided dice; such that: all three dice are numbered the same, and 120 different totals are possible; and the maximum number is as small as possible.

with 7 sided dice, the best possible is: 1, 2, 8, 51, 60, 79, 83

but your challenge is to go one more side.


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#2 superprismatic

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Posted 25 August 2013 - 02:06 AM

Spoiler for to get the contest started


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#3 Anza Power

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Posted 25 August 2013 - 02:41 PM

Spoiler for can go lower

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#4 Pickett

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Posted 26 August 2013 - 08:35 PM

you want to throw three 8 sided dice; such that: all three dice are numbered the same, and 120 different totals are possible; and the maximum number is as small as possible.

with 7 sided dice, the best possible is: 1, 2, 8, 51, 60, 79, 83

but your challenge is to go one more side.

Spoiler for Maybe I have a flaw in my program...
 

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#5 Anza Power

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Posted 26 August 2013 - 08:48 PM

There is no mistake, 84 is the maximum for 7 sides, 120 is the maximum for 8 sides...

In general, (n)*(n+1)*(n+2)/6 is the maximum for n sides.
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#6 Quantum.Mechanic

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Posted 20 September 2013 - 04:06 PM

you want to throw three 8 sided dice; such that: all three dice are numbered the same, and 120 different totals are possible; and the maximum number is as small as possible.

with 7 sided dice, the best possible is: 1, 2, 8, 51, 60, 79, 83

but your challenge is to go one more side.

Maximum sum, or highest numbered side?


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#7 phil1882

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Posted 20 September 2013 - 05:10 PM

highest numbered side


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#8 Quantum.Mechanic

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Posted 25 September 2013 - 02:53 PM

Brute force searches will take a long time. Is there any literature on the structure of solutions?

 

I've looked at sum-free sets, triple-free sets, and prime number of measurement, to name a few, but none seem quite useful in this problem.


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#9 phil1882

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Posted 25 September 2013 - 04:38 PM

http://www.mathpuzzle.com/ no, or at least not much.

we know it for d2 -d7, and if you want to cheat you can look at the solution for d8 at IBM's page, but as far as I'm aware there's no general solution.


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#10 Quantum.Mechanic

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Posted 30 September 2013 - 01:00 PM

It seems that this puzzle is NP-hard and not NP-complete (if I understand this correctly), as there is not an efficient way to prove that the solution is minimal, without an exhaustive search for a better one. (Though a solution can be proved to be valid easily enough, just not minimal.)


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