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Topic: 6 silver coins (Read 999 times) |
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Noke Lieu
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pen... paper... let's go! (and bit of plastic)
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6 silver coins
« on: Sep 13th, 2011, 10:51pm » |
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Over here, we have silver coins : 5c 10c 20c 50c
I have a game, where I give you 6 randomly selected silver coins.
What totals could you recieve?
What would you be prepared to pay in order to play this game?
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| « Last Edit: Sep 14th, 2011, 5:38pm by Noke Lieu » |
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a shade of wit and the art of farce.
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SMQ
wu::riddles Moderator
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Re: 6 silver coins
« Reply #1 on: Sep 14th, 2011, 7:29am » |
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If I've done this all correctly (by pen and paper) there are 84 distinct combinations of coins giving 45 unique totals: all the five-c increments from 30c through 230c except 205c, 240c, 255c, 260c, 270c and 300c. 140c is the most common total, occurring in 225 of the 4096 possible draws. Finally, I would be willing to pay anything up to 125c to play the game repeatedly. (Others might be willing to go as high as 127.5, but I dislike small coins.  )
--SMQ
edit: nope, hadn't done that all correctly--let's try again! corrected two errors in my calculations
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| « Last Edit: Sep 14th, 2011, 9:47am by SMQ » |
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--SMQ
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Grimbal
wu::riddles Moderator
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Re: 6 silver coins
« Reply #2 on: Sep 14th, 2011, 8:03am » |
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Hm... Not sure I agree with you.
Assuming each face value has 1/4 chance to show up, then on average each coin is worth 85/4 = 21.25. Six coins would be worth 255/2 = 127.5 on average.
In theory I would be willing to pay up to 127c.
In practice I should consider the time it takes to play a round, the expenses that go with playing and convert the earnings to an hourly rate. Then see if I am willing to do such a boring job.
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SMQ
wu::riddles Moderator
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Re: 6 silver coins
« Reply #3 on: Sep 14th, 2011, 9:46am » |
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Right you are!  Found and corrected two errors in my work, both in converting coin patterns (e.g. AABBCD) to their proper total value. I believe we are now in agreement.
--SMQ
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--SMQ
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