perplexus.info :: Just Math : Who began with 50 cents?

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

Three bets were made:

(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?

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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            C
After 1st bet:   2*a        b-a          c
After 2nd bet:   2*a        2*(b-a)      c+a-b
After 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     c
5     3     4
10    6     8
15    9     12
20    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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