Nearly precisely a 12 months in the past, I posed a card puzzle here that sparked a frenzy within the feedback part. The answer to that puzzle was so counterintuitive that a number of readers rejected it outright. In honor of the approaching anniversary, it’s time to fire up extra controversy with two extra shocking card puzzles.
Considered one of these I realized from Presh Talwalkar and the opposite from Martin Gardner. So please ahead any hate mail their means.
Did you miss final week’s puzzle? Test it out here, and discover its resolution on the backside of as we speak’s article. Watch out to not learn too far forward if you happen to haven’t solved final week’s but!
Puzzle #46: Coming Up Aces
1. Shuffle a traditional face-down deck of 52 enjoying playing cards after which flip one card at a time face up.
Which card is extra prone to come instantly after the primary ace seems: the king of spades or the ace of spades? In different phrases, you’ll flip over playing cards till you see an ace of any go well with. Is the subsequent card extra prone to be the king of spades or the ace of spades, or have they got equal probability?
2. Reshuffle the identical deck and begin flipping once more. This time, earlier than flipping, you have to guess when the first black ace will seem. Which place within the deck is almost definitely, or are all of them the identical?
I’ll be again Monday with the solutions and a brand new puzzle. Are you aware a cool puzzle that you just assume needs to be featured right here? Message me on X @JackPMurtagh or electronic mail me at gizmodopuzzle@gmail.com
Answer to Puzzle #45: There’s No Place Like Dwelling
Last week’s puzzle requested you to slide into the position of a sports activities statistician. Did you determine how scheduling impacts the NBA championship sequence?
Shout-out to adanarg13 in your well-articulated reply.
In actual basketball, you would argue that the order of the video games issues for psychological causes (e.g., having fun with a streak would possibly improve your probability of successful the subsequent sport), however in our mathematical mannequin it seems the order of the video games doesn’t matter in any respect. In each instances, the Celtics would nonetheless be extra prone to win just because they’ve one additional dwelling sport, even when they find yourself not utilizing it. We’ll argue for the best-of-seven case, however the identical argument extends to different numbers of video games.
The important thing perception is that, even when a staff wins 4 video games earlier than sport seven, then enjoying out the remainder of the video games only for enjoyable couldn’t change the end result of the championship. So we will view the sequence as if they all the time play seven video games it doesn’t matter what after which have a look at who gained extra video games in spite of everything seven have been performed. The staff that performs at dwelling extra usually has an edge.
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