How much money did each player start with?
Posted by admin @ Monday, Mar. 23rd 2009
Jeffrey Z asked:
Al, Bob and Charlie decide to play poker. They agree that when a player
loses a hand, he will pay each of the others an amount equal to the amount
each player already has. Al loses the first hand and pays Bob and Charlie
the amount of money each has. Bob loses the second hand and pays Al and
Charlie the amount of money each has. Charlie loses the third hand and pays
Al and Bob the amount of money each has. At this point, each player has
$8.00.
Al, Bob and Charlie decide to play poker. They agree that when a player
loses a hand, he will pay each of the others an amount equal to the amount
each player already has. Al loses the first hand and pays Bob and Charlie
the amount of money each has. Bob loses the second hand and pays Al and
Charlie the amount of money each has. Charlie loses the third hand and pays
Al and Bob the amount of money each has. At this point, each player has
$8.00.
PLEASE SHOW ALL WORK.
Posted in News
March 24th, 2009 at 8:30 pm
No chips disappear from the game so if there are 24 at the end of the game there are 24 in every round of the game.
The point to grasp is that the recipients double the amount they hold when they win.
So it is a series of retrograde analyses:
After round 3 it is A: 8 B: 8 C: 8 after C has paid out
So before C paid out it must have been A: 4 B: 4 C: 16
So after round 2 it was A: 4 B: 4 C: 16 after B had paid out
So before B paid out it must have been A: 2 B: 14 C: 8
So after round 1 it was A: 2 B: 14 C: 8 after A had paid out
So before A paid out (i.e. at the outset of the game) it must have been A: 13 B: 7 C: 4