The puzzle says, "In my defense, I say that the probability of one player randomly receiving the majority of each kind of face card is reasonable. What is this probability?"
Does the term "face card" in the above statement include the Ace?
Just to check: slapping is allowed during the face-card face-off, right? I've seen both versions of ERS played, but it's been an age or two since I last played.
Q2: are we playing such that won cards are not shuffled and placed at the bottom of the deck? Or do they get shuffled?
Ouch! I totally missed the "exactly" in the Extra Credit section, hence submitting 12459876330000. However, in all cases, writing out the factoradic number is more digits than the decimal, so why not write out 1502852999760_10 rather than 1234569870000000_! ?
Presumably, a player wins when their opponent is out of cards. But what if that happens in the middle of a round. A plays a face card and B,down to only one card, also plays a face card.
Is it over, or is there some mechanism to continue?
Suppose A plays a J, say, and B plays a 5. A wins the round. Now suppose A now puts down a 5, matching the last card played. Does that create a slap, even though there is only one card on the table?
Is there something missing from the Making the Rounds?
Yeah, I'll update to add that you repeat this experiment many, many times and track the overall proportion.
The puzzle says, "In my defense, I say that the probability of one player randomly receiving the majority of each kind of face card is reasonable. What is this probability?"
Does the term "face card" in the above statement include the Ace?
Yes, this includes jacks, queens, kings, and aces in this puzzle (the four kinds of cards relevant to the game of Slap).
Just to check: slapping is allowed during the face-card face-off, right? I've seen both versions of ERS played, but it's been an age or two since I last played.
Q2: are we playing such that won cards are not shuffled and placed at the bottom of the deck? Or do they get shuffled?
Ouch! I totally missed the "exactly" in the Extra Credit section, hence submitting 12459876330000. However, in all cases, writing out the factoradic number is more digits than the decimal, so why not write out 1502852999760_10 rather than 1234569870000000_! ?
"you wanted 120 · (6A + B) to be divisible by 7, which was true if and only if 6A + B was divisible by 7"
Not true! If A=1 and B=8, then 6*1+8=14, divisible by 7.
Nevermind... Just realized in this place both digits must be smaller than 7 (and B smaller than 6). Sorry!
Presumably, a player wins when their opponent is out of cards. But what if that happens in the middle of a round. A plays a face card and B,down to only one card, also plays a face card.
Is it over, or is there some mechanism to continue?
Suppose A plays a J, say, and B plays a 5. A wins the round. Now suppose A now puts down a 5, matching the last card played. Does that create a slap, even though there is only one card on the table?