The numbers all go to 11 - Can You Crack Them?
Are you up for a challenge? A team of footballers donning shirt numbers from 1 to 11 has stumped its coach into submission, proving that it's impossible to divide the players into defenders, midfielders, and forwards in groups whose total jersey numbers are divisible by 11. The problem lies with the sum of shirt number totals for the outfield players - a whopping 65, which can't be evenly divided by 11.
Meanwhile, if you're feeling nostalgic for your school days, you might recall the delightfully simple 11 x times table, where each answer is a palindrome (a number that reads the same backwards as forwards). But what about those of us who've grown out of such simplistic arithmetic? How many more answers from 11 x 1 to 11 x 99 are palindromes? The answer lies in understanding how multiplying by 11 works.
In another mathematical conundrum, a team must create the largest possible 10-digit number using each of the digits 0-9 exactly once and make it divisible by 11. While the biggest number starting with '987654' falls short due to an insurmountable difference of four between its sums, the subsequent arrangement, 9876524130, manages a much closer margin of eleven between its odd-position sum of twenty-eight and even-position sum of seventeen.
Can you solve it? The numbers all go to 11 - will you be able to crack these seemingly intractable mathematical puzzles or leave them to their clever solution.
Are you up for a challenge? A team of footballers donning shirt numbers from 1 to 11 has stumped its coach into submission, proving that it's impossible to divide the players into defenders, midfielders, and forwards in groups whose total jersey numbers are divisible by 11. The problem lies with the sum of shirt number totals for the outfield players - a whopping 65, which can't be evenly divided by 11.
Meanwhile, if you're feeling nostalgic for your school days, you might recall the delightfully simple 11 x times table, where each answer is a palindrome (a number that reads the same backwards as forwards). But what about those of us who've grown out of such simplistic arithmetic? How many more answers from 11 x 1 to 11 x 99 are palindromes? The answer lies in understanding how multiplying by 11 works.
In another mathematical conundrum, a team must create the largest possible 10-digit number using each of the digits 0-9 exactly once and make it divisible by 11. While the biggest number starting with '987654' falls short due to an insurmountable difference of four between its sums, the subsequent arrangement, 9876524130, manages a much closer margin of eleven between its odd-position sum of twenty-eight and even-position sum of seventeen.
Can you solve it? The numbers all go to 11 - will you be able to crack these seemingly intractable mathematical puzzles or leave them to their clever solution.