Did you solve it? The numbers all go to 11

A mathematical enigma that has puzzled many - the number 11. Can we solve it? Well, let's dive into three intriguing problems that will put your math skills to the test.

First up, can we divide a football team of players numbered 1-11 into defenders, midfielders, and forwards, such that the sum of their numbers is divisible by 11? The answer is no. Why? Because the sum of all player numbers except for the goalkeeper (numbered 1) is 65. Since 11 doesn't divide 65, it's impossible to satisfy this condition.

Next, let's explore a math phenomenon that's both fascinating and counterintuitive. When we multiply by 11, many numbers turn out to be palindromes - numbers that read the same backwards as forwards. What's even more remarkable is how many of these palindromes can be generated using just two-digit numbers. By considering different cases, such as matching digits or "staircase" numbers, we find nine additional palindromes beyond the initial four examples.

Last but not least, have you ever wondered what makes a number divisible by 11? It's actually quite simple - all you need to do is alternate adding and subtracting the digits of your number. But how can you create the largest possible 10-digit number that meets this condition using each digit from 0-9 exactly once? The answer, after some careful calculation, is a whopping 9876524130.

These math puzzles may seem simple at first glance, but they reveal some amazing properties and patterns that will challenge your perceptions. Can you solve them all? Only time (and practice) will tell!

I mean, what's the point of even trying to solve these things? It's just gonna be a bunch of numbers and formulas, right? I'm not even sure why they're making such a big deal about it. Like, who needs to divide 11 players into teams or find palindromes with two-digit numbers? Sounds like a total waste of time to me

And don't even get me started on the "answer" to the 10-digit number thing... 9876524130? Who comes up with this stuff? Can you imagine trying to remember that long number or something? It's just gonna be a headache . I'd rather stick to something more practical, like my fantasy football team

omg I love this stuff! the fact that a number like 11 can be so enigmatic is just mind-blowing to me, you know? it's like, what even is going on with numbers?! and I gotta say, who wouldn't want to solve those math puzzles? especially the one about making a 10-digit number divisible by 11... that sounds like a challenge for the ages! and can we talk about how cool it is when you find these weird patterns and properties in numbers? like, what's next?! are there more secrets hiding in plain sight?

You know, I was thinking about this and it got me thinking - life's not always about solving puzzles or finding a 'perfect' answer. Sometimes, we gotta accept the problem as is . Like, can we divide that football team into defenders/midfielders/forwards? Nope! But does that mean we should be disappointed or give up? Nope! We just gotta adapt and move on .

And have you ever thought about how some numbers, like 11, are just a mystery? It's okay to not understand everything. We can still appreciate the complexity and beauty of math problems. Life's full of mysteries we'll never solve, but that doesn't mean we shouldn't keep exploring and learning .

Lastly, did you notice how much time went into finding that 10-digit palindrome? It just goes to show, solving a problem takes patience and practice! But even more importantly, it's the journey, not just the destination, that matters. We should be proud of our efforts, not just the outcome .

omg u guys think these probs r easy lol no way its like, tryin 2 divide those football players into teams w/ sum divisible by 11 thats just not gonna happen and then there's this weird thing about palindromes when u multiply by 11 cant even begin 2 explain how many ways u can make these with 2 digit numbers its crazy! but i gotta ask, what makes a num divisible by 11 tho? all u need 2 do is alternate addin & subtract digits so like, how do u create the biggest possible 10 digit num w/ each digit from 0-9 exactly once? gotta try this out and see what happens

I'M SO EXCITED ABOUT THESE MATH PROBLEMS!!! FIRST OF ALL, I THINK IT'S AMAZING HOW PEOPLE CAN SOLVE SUCH COMPLEX PROBLEMS USING BASIC MATH RULES. LIKE, WHO KNEW THAT ALTERNATING ADDING AND SUBTRACTING DIGITS COULD CREATE A 10-FIGURE NUMBER?!?! ALSO, PALINDROMES ARE SO COOL! I MEAN, IT'S NOT EVERY DAY YOU SEE A NUMBER THAT LOOKS THE SAME WHEN REVERSED. AND THE FACT THAT THERE ARE MULTIPLE WAYS TO GENERATE THEM IS JUST MIND-BLOWING . BUT WHAT REALLY GRIPS ME IS HOW THESE PROBLEMS MAKE YOU THINK OUTSIDE THE BOX. THEY'RE NOT JUST ABOUT SOLVING A MATH PROBLEM, THEY'RE ABOUT UNDERSTANDING THE WORLD IN A WHOLE NEW WAY .

I'm loving these weird math problems . I mean who would've thought dividing a football team into defenders, midfielders, and forwards could be so tricky? And the palindrome thing is wild - nine more palindromes just waiting to be found? I'm definitely going to give that 10-digit number generator a go, can't wait to see what other crazy numbers come out of it!

OMG u gotta check dis out 11's like, the ultimate mathematical mystery . I mean, who knew solving football team lineups could be so hard ? But for real tho, that math phenomenon where numbers turn into palindromes when multiplied by 11 is wild . And can u believe we can create a 10-digit number divisible by 11 using each digit from 0-9 exactly once?! That's like, genius-level stuff . I'm defo gonna try solving these puzzles and share my faves with u

come on, it's not that hard to figure out why you can't divide a football team into defenders, midfielders, and forwards with numbers adding up to 11... the thing is, the sum of all player numbers except for number 1 (the goalie) is 65, which doesn't work with 11 because it's like trying to fit a square peg into a round hole... 11 just ain't gonna cut it

Omg I'm so down for these math challenges I mean who doesn't love a good puzzle to crack The alternating sum thing is so clever and 9876524130 is literally the coolest number ever Can we make these math puzzles more accessible tho? Like, what if we had an online platform where we could share our solutions and discuss them with others Wouldn't that be lit?

omg, the 11 problem is like, soooo weird I was trying to figure out how to divide players into teams without a sum divisible by 11 and I'm like totally stuck 1-10 for defenders, midfielders, and forwards doesn't add up lol 65 is not divisible by 11, what's next? I love how these math puzzles are full of cool patterns and stuff, especially the palindromes. Like, who knew multiplying by 11 could create more palindromes?

omg I'm loving these math puzzles ... like, can we really solve 'em? The football team thing is mindblowin' - 65 doesn't divide by 11, so that's a no-go. And then there's the palindrome thingy... nine more palindromes using just two-digit numbers? That's crazy talk! and who knew alternating digits could make a number divisible by 11? I'm trying to work out the largest 10-digit palindrome but it's giving me some serious brain-twists

I'm intrigued by this stuff . I mean, who knew dividing a football team into defenders and forwards could be so mathematically complex . It's crazy to think about how numbers can be both simple and mind-bending at the same time. And yeah, creating that massive 10-digit palindrome is no joke - it's like solving a giant puzzle piece by piece . I love how these puzzles make you think outside the box and challenge your perceptions. Problem is, I'm not sure if I'll be able to solve them all before the next match day

i think its kinda funny how mathematicians always have to prove something impossible isnt possible lol

anyway, the 11 problem seems pretty interesting. dividing a football team into defenders and forwards and having the sum of their numbers be divisible by 11 just sounds like too much math for me

the palindrome thing tho is cool... who would've thought multiplying by 11 could create so many palindromes?

and can you imagine trying to come up with the largest possible 10-digit number using each digit from 0-9 exactly once? that seems like way more work than just guessing a random number

I love this stuff... I mean, who knew there was so much coolness in numbers right? So the thing is, I'm a big fan of math puzzles, but these ones are like "aha" moments - you think you've got it figured out and then BAM, something sneaky comes along and messes with your head. Like, the football team one, that's just crazy... 65 doesn't divide evenly by 11? No way! And those palindromes with two-digit numbers? That's like a treasure hunt in there. I'm definitely gonna have to dig into all of these and see what else I can find out.

I gotta say, this math stuff is whack . I mean, who even uses 11 as a number? It's like the universe just threw a bunch of numbers at us and said "good luck figuring it out" . But for real though, those palindromes with multiplication by 11 are wild . I never knew math could be so interesting . And that last one about divisibility by 11? I get how to do it now... kinda . Maybe not the largest possible number, but at least I know why 10-digit numbers don't work out as well when using that rule .

You know I think this whole thing about the number 11 is kinda like life itself - we try to find patterns and structure, but sometimes it's just not meant to be divided neatly into boxes . Like, trying to categorize people into defenders, midfielders, and forwards... what if someone doesn't fit into any one category? And then there are these palindromes... how many times do we try to find symmetry in life only to realize it's not that simple? But at the same time, isn't that beauty in its imperfection? And let's be real, solving these puzzles takes practice and patience... kinda like growing up and figuring out who you are.