Football fans, mathematicians, and puzzle enthusiasts, get ready for a brain-twister that will put your skills to the test.
Imagine you're the coach of a football team with 11 players, each wearing a unique shirt number from 1 to 10 (with the goalkeeper sporting the iconic number one). Your task is to divide the team into defenders, midfielders, and forwards in such a way that the sum of their shirt numbers is divisible by 11. Sounds simple, right? Think again.
It turns out, it's not possible to arrange the team in this way. The reason lies in the properties of the number 11 itself. You see, the number 11 has some fascinating characteristics, including being prime and a palindrome. But what makes it truly special is its relationship with palindromic numbers – those numbers that read the same forwards and backwards.
In a clever example provided by mathematicians, we can demonstrate this impossibility. When multiplying 11 by each number from 1 to 9, we get palindromic results: 11 × 2 = 22, 11 × 3 = 33, and so on. However, when we reach the midpoint (56), the result is no longer a palindrome: 11 × 56 = 616.
Now, let's turn our attention to another intriguing challenge. Using each of the digits 0-9 exactly once, can you create the largest possible 10-digit number that is divisible by 11? To solve this puzzle, try using the divisibility rule for 11: add the digits alternately with plus and minus signs (starting with a plus). If the result is a multiple of 11, then your original number is divisible by 11.
Take on this challenge and see if you can come up with the largest possible number that meets these conditions. And remember, at University Maths Schools in the UK, playful mathematical engagement like today's puzzles takes place every day – for students who are passionate about maths and eager to push themselves further.
The puzzle may be tricky, but it's also an opportunity to explore the fascinating world of numbers and their properties. So, take your time, think creatively, and show us what you're made of!
Imagine you're the coach of a football team with 11 players, each wearing a unique shirt number from 1 to 10 (with the goalkeeper sporting the iconic number one). Your task is to divide the team into defenders, midfielders, and forwards in such a way that the sum of their shirt numbers is divisible by 11. Sounds simple, right? Think again.
It turns out, it's not possible to arrange the team in this way. The reason lies in the properties of the number 11 itself. You see, the number 11 has some fascinating characteristics, including being prime and a palindrome. But what makes it truly special is its relationship with palindromic numbers – those numbers that read the same forwards and backwards.
In a clever example provided by mathematicians, we can demonstrate this impossibility. When multiplying 11 by each number from 1 to 9, we get palindromic results: 11 × 2 = 22, 11 × 3 = 33, and so on. However, when we reach the midpoint (56), the result is no longer a palindrome: 11 × 56 = 616.
Now, let's turn our attention to another intriguing challenge. Using each of the digits 0-9 exactly once, can you create the largest possible 10-digit number that is divisible by 11? To solve this puzzle, try using the divisibility rule for 11: add the digits alternately with plus and minus signs (starting with a plus). If the result is a multiple of 11, then your original number is divisible by 11.
Take on this challenge and see if you can come up with the largest possible number that meets these conditions. And remember, at University Maths Schools in the UK, playful mathematical engagement like today's puzzles takes place every day – for students who are passionate about maths and eager to push themselves further.
The puzzle may be tricky, but it's also an opportunity to explore the fascinating world of numbers and their properties. So, take your time, think creatively, and show us what you're made of!
I'm not convinced this is a real problem... I mean, come on, a team of 11 with unique shirt numbers from 1-10? That's just a cop-out. And don't even get me started on the "property" of 11 being prime and a palindrome. That's just basic math.
That's not exactly a clever demonstration, it's just basic multiplication facts. And then they throw in this weird midpoint thing with 56, but that's just a random factoid.
Yeah right. That's not even close to being solvable in a reasonable amount of time. You want me to spend hours trying to figure out if it's possible or not? 
Pass.
but here's the thing mathematicians have shown that when u multiply it with numbers from 1-9 it creates these weird palindromes like 22 or 33 wut kinda math is this 
. And now they're askin' you to create the largest possible 10-digit number that's divisible by 11? It's like they're tryin' to confuse us on purpose 
.
I was waiting in line for the rollercoaster and I started thinking about how some rollercoasters have these insane loops that just make your stomach drop. Like, what even is the physics behind those things? 
. On the other hand, my brain is already exhausted from thinking about rollercoasters all day 
.
. That sounds like a blast! Maybe I'll try to join one someday... or not, because I'd probably just end up getting distracted by all the weird and wonderful math problems 
I'm not convinced this is more than just a fun distraction for math enthusiasts.
! But what's even more mind-blowing is the fact that multiplying 11 by each number from 1 to 9 results in palindromic numbers 
. The puzzle about creating the largest possible 10-digit number that's divisible by 11 is a great way to test our problem-solving skills #NumberTheory 
.
but seriously its awesome 2 see ppl passionate about maths & problem solvin
cant wait 2 c what u come up w/
. The idea that multiplying 11 by each number from 1 to 9 gives us palindromic results is mind-blowing