You realize that I really like puzzles. And I do know that that I really like puzzles. Does it observe that that I do know that that I really like puzzles? No? Philosophers study questions like this within the research of frequent data. To resolve this week’s puzzle, you’ll want to look inside others’ minds and deduce what these minds find out about different minds. Does your thoughts harm but? You realize I do know it does.
Did you miss final week’s puzzle? Test it out here, and discover its resolution on the backside of right this moment’s article. Watch out to not learn too far forward should you haven’t solved final week’s but!
Puzzle #6: Know Your Numbers
Alicia and Bruno are every given a special pure quantity in secret (1 is the smallest pure quantity, 2 is the second smallest, and so forth). They’re then tasked with guessing which ones has the bigger quantity. The next dialog ensues:
Alicia: I don’t know who has the larger quantity.
Bruno: I don’t know both.
Alicia: Upon additional reflection, I stay ignorant.
Bruno: Alas, I’m nonetheless not sure too.
Alicia: Now that you just say that, I really know which of us has the larger quantity!
Bruno: Cool! In that case, I do know what each of the numbers are.
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What numbers were Alicia and Bruno given?
Common knowledge concerns not only what you know, but what you know about what others know about what you know, and so on. It may seem esoteric, but when taken to its logical extreme, common knowledge has bizarre consequences and serves as the basis for many puzzles and even real-world engineering hurdles.
Consider the infamous Two Generals’ Problem. Two generals (let’s call them A and B) belong to the same army, but their troops have been split up and enemy territory separates them. If A’s troops and B’s troops attack the enemy camp at the same time, then they’ll win, but if only A attacks or only B attacks, it won’t be enough to overcome the enemy army, and they’ll lose. So A and B must agree on a time to attack together, and the only way to communicate is to send messages through enemy land that could get intercepted. Here’s how it plays out:
General A writes a message saying, “Let’s both attack at noon tomorrow. Please confirm that you received this message so I know the plan is on.”
General B receives this and replies, “Message received. We’ll attack at noon tomorrow. Please confirm that you received this so I know the plan is on.”
B needs confirmation from A, because if B’s message never delivers, then A won’t know that B agreed to the plan and won’t attack. So if B doesn’t get a confirmation back, he can’t be sure that the plan is on. You probably see where this is headed.
General A: “Yes, I got your message saying that you’re down to attack at noon. So we’re on. Please confirm that you’ve received this.”
B needed this confirmation and wouldn’t attack without it. So of course A needs to know that B got the confirmation he needed so that A isn’t alone at noon tomorrow. This reasoning carries on forever, with each general requiring confirmation from the other in order to be completely assured that they agree.
This isn’t just logical sleight of hand. The Two Generals’ Problem demonstrates a real issue with designing computer protocols when we need two machines to reach consensus by communicating over a potentially noisy channel. How do we guarantee agreement? The answer: we can’t. No algorithm can overcome this barrier, and instead computer scientists recognize it as a limitation of computing networks. Unlike the Two Generals’ Problem, the Gizmodo Monday Puzzle has a solution. Please confirm when you’ve solved it.
Do you know a great puzzle that I should cover here? Send it to me at gizmodopuzzle@gmail.com
Solution to Puzzle #5: Strange Syllables
Last week, I gave you a couple of verbal challenges. First, I requested you to seek out one-syllable phrases that grow to be three-syllable phrases when one letter is added to the tip of them. Shout-out to commenter fffuuuuu, who obtained all three:
- rode -> rodeo
- got here -> cameo
- are -> space
If we have been allowed so as to add the brand new letter wherever fairly than simply the tip, then smile -> simile makes for a pleasant addition to the listing. If we accepted correct nouns, we may embrace ore -> Oreo.
Had been you capable of finding 4 two-syllable phrases which are all homophones of one another? Joost Dantuma wrote to me with a clear instance of a trio of two-syllable homophones: palette, palate, and pallet. The reply with 4 homophones is: carrot, karat, carat, and caret. A “karat” is a unit of the purity of gold, a “carat” is a unit of weight used for diamonds, and a “caret” is the typographical mark ^ above the 6 on most keyboards. One alternate reply that some have put forth is medal, meddle, steel, and mettle, nevertheless official pronunciations for these phrases put completely different sounds on the t’s and the d’s.
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