26 Sep September Puzzler
Digital Agent engineers solve complex puzzles for our customers every day. Can you solve the Puzzle we created for you?
Josh and Chris are solving problems and protecting Atlanta businesses from evil in the voice & data support queue. They have 10 more tickets to go for the day! According to the process, they take turns claiming tickets until there are none left. They can choose to claim either 1 or 2 at a time, but must claim at least 1 per turn. Naturally they decided to turn this into a competition! They agreed that whoever has to take the last ticket is a rotten egg. They both very intentionally make the best moves while giving our customers the best service possible. If Chris goes first, who will win?
Bonus: What if there were 20 tickets to start?
The question specifies that both players always plays optimally. If this is always the case, Josh will always win. His strategy should be to make the opposite of Chris’ play each round. For example, if Chris takes 2 tickets, Josh should take 1. If Chris takes 1 ticket, Josh should take 2. This guarantees that Chris will always end up with the final ticket. Try it with a friend!
If there are 20 tickets, then Chris will always win if he plays optimally. His strategy is to take 1 ticket in the first round, and then copy Josh’s strategy from the first game. In other words, after the first round, Chris will make the opposite play as Josh’s last play. This will guarantee that Josh takes the last ticket.
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