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?
A started with amount a.
B started with amount b.
C started with amount c.
A B C
After 1st bet: 2*a ba c
After 2nd bet: 2*a 2*(ba) c+ab
After 3rd bet: ac+b 2*(ba) 2*(c+ab)
ac+b = 2*b  2*a
3*a  b = c (i)
ac+b = 2*c+2*a2*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 20170906 13:13:58 