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        riddles >> easy >> 6 silver coins
        
(Message started by: Noke Lieu on Sep 13^th, 2011, 10:51pm)

Title: 6 silver coins
Post by Noke Lieu on Sep 13^th, 2011, 10:51pm

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?

Title: Re: 6 silver coins
Post by SMQ on Sep 14^th, 2011, 7:29am

If I've done this all correctly (by pen and paper) there are [hide]84[/hide] distinct combinations of coins giving [hide]45[/hide] unique totals: [hide]all the five-c increments from 30c through 230c except 205c, 240c, 255c, 260c, 270c and 300c[/hide]. [hide]140c[/hide] is the most common total, occurring in [hide]225[/hide] of the 4096 possible draws. Finally, I would be willing to pay anything up to [hide]125c[/hide] to play the game repeatedly. (Others might be willing to go as high as [hide]127.5[/hide], but I dislike small coins. ;))

--SMQ

edit: nope, hadn't done that all correctly--let's try again! corrected two errors in my calculations

Title: Re: 6 silver coins
Post by Grimbal on Sep 14^th, 2011, 8:03am

Hm... Not sure I agree with you.
[hide]
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.
[/hide]

Title: Re: 6 silver coins
Post by SMQ on Sep 14^th, 2011, 9:46am

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