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# All numbers showing

18 replies to this topic

### #1 bonanova

bonanova

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Posted 23 January 2013 - 10:27 AM

You throw m fair six-sided dice and bet that all numbers from 1 to 6 will show at least once.
What is the smallest value of m that gives you a winning bet on average?
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Vidi vici veni.

### #2 TimeSpaceLightForce

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Posted 23 January 2013 - 05:01 PM

Spoiler for start

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### #3 superprismatic

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Not just Prismatic

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Posted 23 January 2013 - 05:40 PM   Best Answer

Spoiler for I get

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### #4 TimeSpaceLightForce

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Posted 23 January 2013 - 06:33 PM

Spoiler for low attemp

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### #5 Prime

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Posted 24 January 2013 - 12:19 PM

I can get an answer, but no simple explanation. But that should do for everyday gambling needs.

Spoiler for The smallest m is...

Edited by Prime, 24 January 2013 - 12:27 PM.

• 1

Past prime, actually.

### #6 bonanova

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Posted 25 January 2013 - 08:59 AM

I can get an answer, but no simple explanation. But that should do for everyday gambling needs.

Spoiler for The smallest m is...

Ah, but there is one. No correct answers yet.
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Vidi vici veni.

### #7 superprismatic

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Posted 26 January 2013 - 01:14 AM

I can get an answer, but no simple explanation. But that should do for everyday gambling needs.

Spoiler for The smallest m is...

Ah, but there is one. No correct answers yet.

Since I got my answer using Prime's method, I'll now consult Strunk and White to see what else the OP could possibly mean.  Possibly a weighted average m?  Anyway, I must look in the basement for that copy of Strunk and White which I know is down there somewhere.

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### #8 phil1882

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Posted 26 January 2013 - 02:19 AM

Spoiler for

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### #9 plainglazed

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Posted 26 January 2013 - 02:31 AM

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### #10 bonanova

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Posted 26 January 2013 - 02:44 AM

Yes. Simple concept that cuts thru all the computational complexity.
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Vidi vici veni.

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