You know I love puzzles. I know you know I love puzzles. Does it follow that you know I know you know I like puzzles? no? Philosophers study questions like these in monographs general knowledge. To solve this week’s puzzle, you will need to look into other people’s minds and deduce what these minds know about other people’s minds. Does your mind hurt yet? You know I know she does.
Did you miss last week’s puzzle? check it out here, and find its solution at the end of today’s article. Be careful not to read too far if you haven’t solved last week yet!
Puzzle #6: Know your numbers
Alicia and Bruno are each secretly given a different natural number (1 being the smallest natural number, 2 being the second smallest, and so on). Then they are tasked with guessing which of them has the largest number. The following conversation ensues:
Alicia: I don’t know who has the bigger number.
Bruno: I don’t know either.
Alicia: After some more thought, I’m still clueless.
Bruno: Unfortunately, I’m still not sure either.
Alicia: Now that you’ve said that, I really know which of us has the bigger number!
Bruno: Awesome! In this case, I know what both numbers are.
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What numbers were given to Alicia and Bruno?
General knowledge isn’t just about what you know, it’s about what you know about what other people know about what you know and so on. It may seem esoteric, but when taken to its logical extremes, common knowledge has bizarre consequences and serves as the basis for many puzzles and even engineering obstacles in the real world.
Consider the infamous generals problem. Two generals (let’s call them A and B) belong to the same army, but their forces are split and enemy territory separates them. If A forces and B forces attack the enemy camp at the same time, they will win, but if only A or B attacks, it will not be enough to overwhelm the enemy army, and they will lose. So A and B must agree on a time to attack together, and the only way to communicate is to send messages across enemy territory that can be intercepted. Here’s how it’s done:
Gen. A writes a letter saying, “Let’s attack at noon tomorrow. Please confirm you received this message so I know the plan is in play.”
General B receives this and replies, “Message received. We will attack at noon tomorrow. Please confirm you received this so I know the plan is in play.”
B needs confirmation from A, because if B’s message is never delivered, B will not know that B agreed to the plan and will not attack. So if B does not get confirmation, he cannot be sure that the plan is running. You might see where this is going.
Gen. A: “Yes, I got your message saying you would attack at noon. So we’re in. Please confirm you received this.”
B needed this confirmation and would not attack without it. So of course A needs to know that B got the confirmation he needs so that A won’t be alone at noon tomorrow. This thinking goes on forever, each year requiring confirmation from the other to be absolutely sure they agree.
This is not just a logical sleight of hand. The two generals problem illustrates a real problem in the design of computer protocols when we need two machines to reach consensus by communicating over a potentially noisy channel. How do we guarantee agreement? Answer: We can’t. No algorithm can overcome this barrier, and instead computer scientists recognize it as a limitation of computing networks. Unlike the generals’ problem, Gizmodo’s Monday puzzle has a solution. Please confirm when it is resolved.
Do you know of a cool mystery I have to cover here? Send it to me at gizmodopuzzle@gmail.com
Solve puzzle number 5: strange syllables
Last week, I gave you a pair of Verbal challenges. First, I asked you to find single-syllable words that become three-syllables when one letter is added to the end of them. shout out to Commentator fffuuuuuwho got all three:
- rode -> rodeo
- came -> cameo
- is -> area
If we’re allowed to add the new character anywhere instead of just at the end, smiley -> simile is a great addition to the list. If we accept proper names, we can include ore -> Oreo.
Did you manage to find four two-syllable words that are homophones for each other? Joost Dantuma wrote me with a clear example of a triple It has two homologous syllables: a slab, a palate, and a pallet. The answer with four homophones is: carrot, carat, carat, and intercalation. “carat” is the unit of purity of gold, “carat” is a unit of weight used for diamonds, and “caret” is the typographic mark ^ Top 6 on most keyboards. One alternative answer some have put forward is medallion, tackle, metal, and hardness, however the official pronunciation of these words places different sounds on the letters t and d.
(tags for translation) Bruno Alas