You’re right that this is not what I had in mind, but I think you’ve made a great case for it.
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Jack Murtagh's discussions
I find the solution elegant too. It’s nice that it avoids explicitly dealing with angles of the hands or modular arithmetic. Read more
Sorry if my wording was clumsy. This interpretation is correct. If you swap the hands on a normal clock at 4:00, the resulting position won’t display a valid time for the reasons you describe.
You’re right that the obvious answers to the question occur when the hands overlap, but there are others!
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The right-most digit of the answer must describe the number of 9s in the number. The right-most digit of 9,000,000,000 is zero, but there are not zero nines in the number.
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Good attempt. What if instead of taking a king high straight flush on my first turn I take four kings? Then you can’t get an ace high straight flush and I’m threatening to get a king high straight flush on my second turn.
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Yes you’re right. Full marks to anyone who said triplets, quadruplets, or above.
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It seems hard for player 1 to force a win, but they can. You say “there will always be a highest possible straight flush left in the deck,” which is true, but that’s not necessarily the highest straight flush left in the game. Player 2 does not have access to the five cards that Player 1 picked in the first round.
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Ties go to me. So if you pick a royal flush on the first turn, then I will pick a royal flush of a different suit and hang on to my cards. I win in this case. Read more
The four corners of your bar are all ones.
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Nicely done, this was exactly my solve path as well. The two person case fell quickly, largely because there weren’t that many things you could try. But it wasn’t at all clear how to extrapolate to 3+ people. I’m glad you stuck with it. I think this solution is pretty cool.
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You’re on a very good path.
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There’s a definite way to win, it’s not probabilistic. I’ll start with two small hints and maybe come back with a bigger hint if everybody is still stumped.
Hint 1: There’s a reason the puzzle uses the digits 0 to 9 instead of 1 to 10. The group could win in either case, but the underlying reasoning is more natural… Read more
No communication of any kind is allowed once the cards are distributed. If you like, you can imagine each person isolated in their own cell and the madman tells them each separately what every other person’s number is. Then they have to submit their shout. Communication is only allowed before the cards are… Read more
Everybody could have an 8 except for the eighth person in line. Then nobody would be correct. So this proposal doesn’t quite work.
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Ohh EAUC is a good one. I thought the EAU lineup was going to be a quick giveaway, but it had me stumped for a while.
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Yeah, there is a real non-acronym word with the letters PTC in a row.
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Oh nice find! That actually wasn’t the intended answer, but it does fit the pattern.
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Very interesting question. I can think of two ideas to make the game fairer. One is to design it so that perfect play leads to a draw. For example, I think if the teams can only take two or three flags and you stipulate that a draw occurs if exactly one flag remains, then perfect play leads to a draw. This puts the… Read more
Nice, thank you.
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Definitely a math question! Model the teams as achieving their scores probabilistically. Since they’re perfectly matched, they’ll have the same probabilities of scoring various amounts. From this information alone you can deduce the chance that the team who trails at halftime comes back to win.
By the way, do you know… Read more