Did you solve it? The London cab that rode into history

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The London cab that rode into history: Unraveling the secrets of 1729.

A peculiar number has captivated mathematicians and puzzle enthusiasts alike - 1729. This "taxicab number" is famously known for its unique properties, which have fascinated minds for centuries. Today, we'll delve into three mind-bending puzzles that are loosely based on this iconic year, designed to test your problem-solving skills.

The first challenge: finding the smallest number expressible as the sum of a pair of squares in two different ways. After some careful consideration, the answer is 50 - achieved by pairing 1^2 + 7^2 and 5^2 + 5^2. This solution reveals that with patience and persistence, even the most seemingly complex problems can be cracked.

Next up, we have a puzzle of strips and triangles. With five wooden strips of varying lengths (1cm, 2cm, 7cm, 17cm, and 29cm), can you create a triangle using only three of these strips? The answer lies in the length of the seventh strip. By carefully selecting this mysterious piece, you'll be able to prevent the formation of any triangles. However, the exact lengths are unknown - for now.

In another test of logic, we're presented with four numbers (a, b, c, and d) that can be whole numbers or fractions. These numbers have six possible multiplication combinations. With five known products (2, 3, 4, 5, and 6), the final product is waiting to be discovered. By carefully analyzing these combinations, it becomes clear that two pairs must multiply to produce the same result - leading us to a tantalizing calculation: 12.

These three puzzles are just a glimpse into the fascinating world of mathematics and problem-solving. Who knows what secrets lie hidden within the digits of 1729? Perhaps only the cleverest minds will be able to unravel them.
 
I'm loving these puzzles! The fact that 1729 has been captivating mathematicians for centuries is just mind-blowing 🤯. I mean, think about it - a number that can be expressed in so many different ways, yet still has secrets waiting to be uncovered.

The first puzzle was super interesting - finding the smallest number that's the sum of two squares in multiple ways. I like how they used simple examples like 1^2 + 7^2 and 5^2 + 5^2 to make it tangible. And yeah, with patience and persistence, even crazy-hard problems can be solved.

The strip-triangle puzzle was a bit tricky, though - I love how they left out the lengths of the strips! That's like leaving a trail of breadcrumbs for us to follow. And the seventh strip being the mystery piece? Genius 🔮.

Lastly, the logic puzzle with six combinations and five known products had me hooked. The part where two pairs multiply to give the same result was so cool - it's like solving a hidden pattern 🎨. 12 is still an unknown, but I'm confident that someone will crack it soon! 💡
 
🤔 you know, this reminds me that life's got these crazy patterns too 🌐 like, think about it - we're all searching for ways to make sense of stuff, just like mathematicians trying to solve puzzles 🧩 and sometimes the answers lie right in front of us... but we gotta pay attention & keep trying 💡. And yeah, 1729 might be a weird number, but at the end of the day, it's all about figuring out how things fit together 😊.
 
I'm like "math problems, yeah right! 🤣" but seriously, who knew maths could be soooo cool? I mean, I just figured it was like, numbers and stuff... 😂 but nope! This 1729 number has been puzzling people for centuries and now we got these crazy challenges to solve 'em. I'm all about the 50 - that's like my new goal, gonna practice pairing squares till I get it right 🤓. And omg, triangles with strips? That sounds like a real-life game of Tetris... or maybe not, but still cool! 👍
 
🤓 I gotta say, this "taxicab number" 1729 is straight fire 🔥! Like, who wouldn't wanna crack some mind-bending puzzles based on it 🧩? The first one's pretty cool - finding a pair of squares that sum up to the same amount 📝. I'm no math whiz, but even I thought it was possible 😎.

And can you believe there's actually a "mystery strip" 🤔 that's crucial to forming triangles?! Like, what if I had one of those strips in my pocket right now? 🔍 I'd totally wanna try and figure out its length ASAP 💪.

The puzzle with the fractions seems pretty tricky too 🤯. I love how they say "with patience and persistence" - sounds like a mantra for any math enthusiast 👏. And that final calculation... yeah, it's like, whoa 😲! Maybe someone out there can crack it 🔓
 
omg i'm still trying to wrap my head around that 50 thing 🤯 like how do u come up with that kinda math stuff? it's so cool but also super confusing at the same time lol

and idk about those triangle strips thingy - how r u supposed to figure out what length makes a triangle not work tho? i need more info on that one 😂

but 12 is def a legit question - how can two pairs of numbers multiply to the same result? that's like a math mystery 🧐
 
🤔 i think its cool that maths has these weird secrets like 1729, makes u wanna dive in & try solve puzzles 🧩💡 the way they did with 50 - pairing squares & triangles too, shows u dont have 2 b a genius 2 figure it out, just be patient n try different combos 💻
 
OMG u guys I was at the British Museum last yr & I saw this old London cab exhibit 🚕🤯 it had all these cool math puzzles on the walls & I was like wow I need to try those rn 🤔 I've been trying to solve the strip puzzle tho its giving me major brain fart 😂 did u guys know that 1729 is like a famous number in math? 🤓
 
I think its kinda weird that people get so excited about math problems based on random numbers like 1729... but I guess its cool for those who love puzzles 🤔. Its not every day you see puzzles designed around an old number from history, right? Like, I wonder what other secrets or stories are hidden in old dates and stuff 👀
 
🤔 I'm not sure about this "taxicab number" business, seems like a made-up term to me. Can anyone explain why 1729 is so special? 🚕 Is it really just a random year or is there some hidden math magic behind it? The puzzles they presented seem quite simple and straightforward... I mean, who wouldn't be able to figure out that 1^2 + 7^2 = 50 and that the missing strip length would prevent a triangle from forming? 😒
 
OMG, like I'm actually fascinated by this 1729 thing! The idea that it's been a mind-bender for centuries is already kinda cool... but then these puzzles show up and I'm HOOKED 🤯📝. Like, who wouldn't want to crack the code of something that's been stumping people for so long? And 50 as the answer to that first puzzle? Genius! 😎 The more I read about this, the more I wanna dive in and try solving these puzzles myself... but at the same time, I'm like "wait a minute, what's up with the seventh strip length?" Like, is it just me or does that seem kinda like a wild card? 🤔📝
 
idk why everyone's so obsessed with these "puzzles" 🤔... like, i get it, they're fun for math nerds and all, but is there really anything profound going on here? 50 as a sum of two squares seems kinda obvious once you think about it. and the triangle puzzle just feels like a weird trick - what's the point of that? 🤷‍♂️
 
🤔 the taxicab number thing is actually pretty interesting, I guess. I mean, who knew a random year could have so many weird and wonderful properties. 📊 it's like the universe decided to throw a math party in 1729 and invite everyone. 🎉 anyway, these puzzles are kinda fun, but not too hard or anything... I'd rather be solving real-world problems than playing with numbers all day 😴
 
I'm loving this stuff 🤔. Like, I know 1729 is a big deal for math nerds, but honestly, who wouldn't want to spend their time solving puzzles all day? 😊 It's like, you gotta admire the complexity of these problems - they're not just about numbers, it's about how they relate to each other.

Here's my take on the first puzzle: finding that number 50 expressed as a sum of two squares. I think it's cool how we can break down a problem into smaller parts, like in this case, pairing up those squares. It's all about trial and error, you know? And then there's this puzzle with strips and triangles... 📏 That one's got me stumped for now. I mean, what if the seventh strip is, like, the key to it all?

The last one's got me thinking... four numbers, six possible combinations... it's like a math game of Tetris or something! 🎮 Do you think we can figure out that final product? Maybe by analyzing those known products and seeing how they relate to each other.

Anyway, I'm gonna keep working on these puzzles. It's like, my brain's on fire with curiosity right now 🔥.
 
You know, I'm really loving these puzzle challenges 💡. It's amazing how something as simple as math can lead to such mind-bending problems. I mean, who wouldn't want to figure out a way to create a triangle with just three of those strips? 🤯 And 50 being the sum of two squares in different ways is pretty cool too... I'm definitely going to have to give these puzzles a try myself! 👍
 
I'm loving these old-school puzzles 😊. I mean, who needs a smartphone when you've got some brain-twisters like this to keep you busy? The London cab number thing is pretty cool - I didn't know 1729 was so special 🚕. I tried the first puzzle and I'm stumped on the second one... how do they figure out if it's possible or not without knowing the length of that mysterious strip? 🤔 And this last one, finding that final product with just five known products? Not easy to wrap your head around 📝. Anyway, great stuff for people like me who love a good math challenge 😄.
 
I'm loving this 🤓 news about the London cab that rode into history! You know, I was thinking, if you can solve these puzzles, it's like solving a mystery - and who doesn't love a good mystery? 💡 It's not just about numbers and math, but also about being patient and persistent, which are super valuable life skills 📚. And the puzzle with the strips of wood? That one has me stumped 😂 - I wonder what kind of thinking goes into solving it. Maybe someone out there is a genius waiting to be discovered? 💥
 
[Image of an astronaut in space looking puzzled 🚀😕]

math problems r like trying to find the meaning of life but with numbers instead of answers 👀💭

[ GIF of a person stuck in an infinite loop, repeatedly solving math problems 💻🔄 ]

anyone else have nightmares about 1729 being the key to unlocking all math secrets? 😳🔓
 
Ugh, I'm so over these "puzzles" 🤯 they're just a bunch of weird maths problems designed to mess with your brain. Can't we have something more practical or interesting for once? Like, have you guys tried to figure out how the forum's algorithm works? Now that's a real challenge 😂
 
🤔 So I was reading about this weird "taxicab number" 1729 and honestly, I'm not sure how much I buy into all these puzzles. Like, don't get me wrong, they're cool and all, but aren't these just classic math problems we've seen before? 📚 Still, I do love the creativity behind 'em - using squares and strips to solve for unknowns... it's actually kinda refreshing to see people still stumped by this stuff. What really got me though was how these puzzles are kinda like life itself - you need patience, persistence, and sometimes just a little bit of lateral thinking 🤯.
 
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