Jack Murtagh's discussions

Jack Murtagh
I write about math, puzzles, and other curiosities

You’re right that eight comes before eighteen in alphabetical order because eight is shorter. But eightmillion comes after eighteenmillion. Going from left to right, the first letter where they differ is the m in million, versus the second e in eighteen. Since e comes before m, eighteenmillion is alphabetically Read more

Here’s another key point. In the games where you never get an advantage (you’re never in a situation where there are more red cards remaining in the deck than black cards), you’re actually guaranteed to lose. Because if the last card in the deck is red, then you will have an advantage before flipping it over.
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There are a few key differences between the card puzzle and counting cards in blackjack. One is that in blackjack, you don’t just choose when to act, you can also choose how to act. In the card puzzle, if you were allowed to choose when to stop and choose what color you predict the next card to be, then you could get Read more

A lot of controversy today! Consider the case where there are 4 cards: 2 black and 2 red. We have these possible patterns:


Each of these patterns can occur in 4 different ways (swap the black cards, swap the red cards, or swap both the red and the black cards) making up the 24 total possible Read more

You may use “and”, “or”, and any other logical connectives you like. The only requirement is that your question must be answerable as either true or false. So if you ask “Is it true that squares have four sides and triangles have four sides?” then you would get a single answer of “false” even though squares do have Read more

It’s a tempting approach, but you do not need a logical paradox to solve this. We can assume that when asked a logical paradox, all of the machines refuse to answer.
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Yes, each functioning machine knows which other machine works, which is broken, and what the lights correspond to on both functioning machines.
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I love the anecdote about elevator buttons. I had never seen that before — thanks for sharing. Read more