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2-player game outcome?

Quick find code: 23-24-619-66212237

vonSageworth

vonSageworth

Posts: 1,752 Mithril Posts by user Forum Profile RuneMetrics Profile
You have 15 cups. (Doesn't have to be cups, it can be buttons, toothpicks, pencils, etc).

You and the other player can remove 1, 2, or 3 cups, no more.

You take turns removing cups.

How can you insure you take the last cup?

(Hint)

The hint says: Select 1-3 cups so the remaining total is dividable by 4. Your first move is to take 3 cups. So the remaining is 12


I've tried this several times and the last few equals 4. So no matter how many I take the other player ends up with the last one.
Music is the Heartbeat of the World


Let's flip a coin; heads I win, tails you lose. Fair enough?

18-Apr-2021 17:41:44 - Last edited on 18-Apr-2021 23:49:19 by vonSageworth

vonSageworth

vonSageworth

Posts: 1,752 Mithril Posts by user Forum Profile RuneMetrics Profile
Megycal said :
I think you have to make sure you are the one to get to 4 objects remaining. I don't know how you can be sure this happens. Sorry

Yes, I can get to 4 objects remaining, however, the most I can take is 3 objects leaving one object left for the other player. I've tried several different ways, but the outcome is always the same.

I don't know if there is a mathematical equation here or not.
Music is the Heartbeat of the World


Let's flip a coin; heads I win, tails you lose. Fair enough?

20-Apr-2021 23:53:49

Icy Spring

Icy Spring

Posts: 3,248 Adamant Posts by user Forum Profile RuneMetrics Profile
You use your first move to reduce the number of cups to a number that is divisible by 4, then use your subsequent moves to make the number of cups removed every 2 turns equal to 4:

15 -> Choose 3
(Opponent is left with 12)
(Opponent removes cups)
11 -> Choose 3
10 -> Choose 2
9 -> Choose 1
(Opponent is left with 8)
(Opponent removes cups)
7 -> Choose 3
6 -> Choose 2
5 -> Choose 1
(Opponent is left with 4)
(Opponent removes cups)
3 -> Choose 3
2 -> Choose 2
1 -> Choose 1

If you pick wrong at any turn you are guaranteed to lose.

21-Apr-2021 00:06:01 - Last edited on 21-Apr-2021 05:10:12 by Icy Spring

vonSageworth

vonSageworth

Posts: 1,752 Mithril Posts by user Forum Profile RuneMetrics Profile
@Icy Spring...

I played the puzzle using the 3-2-1 method. The first time I lost, but the second time I won. Thanks for helping me.

The moves of my opponent was random generated, so the walkthrough wasn't very helpful, except to say that my first move should be 3 items.

Problem solved. I opened the next door.
Music is the Heartbeat of the World


Let's flip a coin; heads I win, tails you lose. Fair enough?

22-Apr-2021 09:16:32 - Last edited on 22-Apr-2021 09:18:08 by vonSageworth

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