# Three Cowboys, 11 bullets

While seeing a previous question not very well explained, a variant has emerged. I guess it wasn't intended by the OP but I find the variant even more interesting than the original one.

Let me explain the variant: A gun battle is about to happens. The participants are Leo, Kenny and Jack. All three are excellent shooters and as they don't want to waste any bullet they decide to make up some rules:

(1) They will shoot one after another and are forced to shoot on someone.
(2) When a player is injured others must shoot (keeping the same order) on him with the intention of killing and the injured player can't shoot anymore.
(3) On their six bullet guns, Leo will have all six bullets, Kenny will have 3 bullets separated by an empty slot between each and Jack will have only 2 bullets separated by 2 empty slots.
(4) The order is determined by the number of bullet given at the start, so Jack will fire first, then Kenny and finally Leo.
(5) Missing a shot is such a waste that it is not allowed.

Can you guess what will happen if they all play perfectly?

(6) They are allowed to change the alignment of bullets in their barrel as long as it matches rule 3
(7) As they are super-skilled they may choose between injuring someone or killing him (respecting rule 2)

• Two questions: 1) what causes injury and what causes death ? 2) What is the alignment of the guns' barrels (i.e. : are the first shots blank or not ?) – Keelhaul Jan 18 '18 at 14:36
• Also, I'm pretty sure Kenny will die. – Keelhaul Jan 18 '18 at 14:36
• Well they can choose the alignment as long as it isn't against the rules. And shooters are skilled so a bullet can injured or kill as they choose. But if someone is already injured they have to shoot to kill (rule 2) [ in other words they will kill him as long as they have a bullet fired]. – Untitpoi Jan 18 '18 at 14:39

For the sake of explanation, let's say an empty slot is a blank.

Let's say that Jack put a real bullet as his first shot:
- If Jack kills Leo, Kenny kills him OR Kenny blanks, Jack blanks and Kenny kills Jack.
- If Jack kills Kenny, Leo kills him.
- If Jack injures Kenny, Leo finishes him off, Jack shoots blank and Leo kills Jack.
- If Jack injures Leo, Kenny finishes him off, Jack blanks, Kenny blanks, Jack blanks again and Kenny kills Jack OR Kenny blanks, Jack blanks, Kenny finishes off Leo, Jack blancks, Kenny blanks and Jack kills Kenny.

So, if Jack shoot a real bullet first, he should injure Leo and hope Kenny has put a blank first in his gun.

Now, if Jack has put a blank as first shot, what will Kenny do ? Let's assume Kenny has a real bullet first :
- If Kenny kills Leo, Jack kills him OR Jack blanks (his bullet in 3rd position), Kenny blanks and Jack kills Kenny.
- If Kenny kills Jack, Leo kills him.
- If Kenny injures Leo, Jack finishes Leo, Kenny blanks, Jack blanks, Kenny kills Jack OR Jack blanks (his bullet in 3rd position), Kenny blanks, Jack finishes off Leo, Kenny kills Jack.
- If Kenny injures Jack, Leo finishes Jack, Kenny blanks, Leo kills Kenny.

So, in that case, Kenny is assured to win if he put a real bullet and shoot to injure Leo.

In conclusion, Kenny will put a bullet as his first shot.
- If Jack has done the same, he will injure Leo, Kenny finishes Leo, Jack blanks, Kenny blanks, Jack blanks again and Kenny kills Jack => Kenny wins!
- If Jack has put his bullet as his second shot, Kenny will injure Leo, Jack finishes Leo, Kenny blanks, Jack blanks, Kenny kills Jack => Kenny wins!
- If Jack has put his bullet as his third shot, Kenny will injure Leo, Jack blanks, Kenny blanks, Jack finishes Leo, Kenny kills Jack => Kenny wins!

Long story short: Kenny put a bullet as his first shot and wins by following this strategy.

However, if Jack knows Kenny is a perfect player and will put a bullet as first shot, he knows he will die no matter what. As an act of pure spite, he could then kill Kenny, because Jack is a bastard!

• And if I'm right, then I was wrong in the comments: Kenny (surprisingly) doesn't die ! – Keelhaul Jan 18 '18 at 15:26
• I added an alternative ending having Kenny killed if Jack decides to throw away every little hope he could have to win (i.e., knowing Kenny will play perfectly). – Keelhaul Jan 18 '18 at 15:38
• Nice epilogue! Kenny surviving is such a contradiction to logic. – Untitpoi Jan 18 '18 at 15:39