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 Who began with 50 cents? (Posted on 2017-09-06)

(1) First, A won from B as much as A had originally.
(2) Second, B won from C as much as B then had left.
(3) Finally, C won from A as much as C then had left.

The three players ended up with equal amounts of money.

Who began with 50 cents?

 No Solution Yet Submitted by Jer No Rating

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 solution | Comment 2 of 3 |
A started with amount a.
B started with amount b.
C started with amount c.

`                 A          B            CAfter 1st bet:   2*a        b-a          cAfter 2nd bet:   2*a        2*(b-a)      c+a-bAfter 3rd bet:   a-c+b      2*(b-a)      2*(c+a-b)`

a-c+b = 2*b - 2*a
3*a - b = c            (i)

a-c+b = 2*c+2*a-2*b
3*b - a = 3*c          (ii)

6*b - 10*a = 0         (ii) - 3 * (i)

3*b = 5*a

`b     a     c5     3     410    6     815    9     1220    12    16...50    30    40`

B started with 50 cents, as 50 is not divisible by 3 or by 4.

 Posted by Charlie on 2017-09-06 13:13:58

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