Originally posted by AThousandYoung
Each player touches 1/n from the end.
Everyone gets equal amounts of bread.
We can see that is wrong with 3 players
Stick length is 12
if player A goes at 1/3rd of 12 (4) then
Player B selects 8.1
If C plays between A and B he gets 4.1/2 = 2.05
If C plays next to B (nearer end) say at 8.2, then he gets 3.85
If C plays next to A (nearer end), say at 3.9, then he wins 3.95
So, C cuts inside A leaving A with 2.1, B with 5.95, and C with 3.95
A has clearly lost, B has clearly won.
My algorithm predicts A should go at 12/4 = 3
If B tries the same trick, and goes at 9.1 then:
If C goes outside B at 9.2 then he gets 2.85
If C goes in between A and B he gets 6.1/3 = 3.05
and if C cuts inside A, say at 2.9 then he gets 2.95
So C plays in between A and B, and due to the rules plays exactly in between them at 6.05
Now B gets 4.425
A gets 4.525
and C gets 3.05
A has won
So my algorithm is best for A