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I visited my younger cousins, John and Edmund, recently, and found them playing an interesting game. They would take turns to call out numbers until one of them declared themselves the winner. They would also alternate the person who would start the game.

Here are examples of some of the games they played (I've written John's answers in italics and Edmund's answers in bold)

3, 2, 3, 4, 4, 5, 5, 2, 3, 3, 4, 2, 2, 4, 5, 7, 6

At this point, John declared himself the winner.

2, 3, 2, 2, 1, 4, 1, 5, 6, 3, 5, 3, 3, 1, 1, 2

Again, John declared that he won at this point. After some consideration, Edmund reluctantly agreed.

As the afternoon wore on, the games tended to get longer. Here was another one won by John

1, 4, 1, 1, 4, 3, 5, 2, 2, 3, 3, 1, 2, 2, 4, 4, 3, 4, 3, 3, 2

Edmund was clearly having some difficulty beating his older brother but, eventually, he came through in the longest game I had witnessed.

4, 3, 5, 4, 6, 7, 4, 5, 3, 2, 6, 5, 5, 3, 1, 4, 5, 3, 3, 4, 5, 1, 4, 3, 7, 7, 1, 7, 1, 1, 7, 7, 1, 6, 6, 6, 6

"Yes! I win!" exclaimed Edmund.

I didn't really understand the rules of the game yet but I had a strategy I wanted to try and asked John if I could join in.

"Sure", said John, "4".
"4", I responded
"3", said John.
"3", I responded with confidence.
"2. I win!", exclaimed John.

I was a bit dumbfounded and looked over at Edmund who was chuckling in the corner. I couldn't understand how my strategy had lost so quickly. I accused them of making it all up but they insisted that it was a real game.

Can you explain how the game works?

Hint

John and Edmund's game is not their own creation, they are just playing the game in an unusual way.

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  • $\begingroup$ Would it give too much away to say why the knowledge tag is there? There's no indication in the text that it should be. $\endgroup$ – deep thought Feb 1 at 15:51
  • $\begingroup$ @deepthought I debated whether or not to include it. You can take it as a very small hint. The knowledge is not entirely necessary but is incredibly useful to determine the answer. $\endgroup$ – hexomino Feb 1 at 16:59
  • $\begingroup$ rot13: Fvapr gur ahzoref hfrq ner sebz bar gb frira, vf vg snve gb nffhzr gung gurer vf gur hfr bs bpgny ahzoref? $\endgroup$ – Daniel Baliki Feb 1 at 18:34
  • $\begingroup$ @hexomino any chance of a hint? thanks! $\endgroup$ – Omega Krypton Feb 4 at 4:35
  • $\begingroup$ @DanielBaliki that is a good observation to make but it has nothing to do with what you suggested. $\endgroup$ – hexomino Feb 4 at 10:03
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I think they are playing

Connect Four

with the numbers representing

which column they are dropping their pieces into (the numbering appears to be as though they are sitting on the same side of the board, so they are both counting "1" as the leftmost column).

The final game gives John

three unbounded pieces along the bottom, with no possible way for the opponent to win, so although the game hasn't technically played to a conclusion yet, it can't go any other way.

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