"Funny formation You are the coach of a football team, whose players have shirt numbers 1 to 11. The goalkeeper wears 1. You must divide the others into defenders, midfielders and forwards. You would like to arrange your team so that the sum of the shirt numbers in each group (defenders, midfielders, forwards) is divisible by 11? Give an example, or prove it isn't possible."
"Pals or not When we first learn our times tables, the 11-times table feels delightfully simple: 11 1 = 11 11 2 = 22 11 3 = 33 11 9 = 99 All the answers are palindromes (numbers that read the same backwards as forwards). If we carry on, up to 11 x 99, how many more answers are palindromes? [Hint. At least one! For example, 11 56 = 616.]"
"Big divide Less well known than other divisibility rules, there is a simple way to test for divisibility by 11. Take the digits of a number and add them alternately with plus and minus signs (starting with a plus). If the result is a multiple of 11 (including 0), then the original number is divisible by 11. For example, for 132 we get 1-3+2 = 0, so 132 is divisible by 11."
Three puzzles explore arithmetic properties tied to the number eleven. Puzzle 1 asks whether players numbered 2–11 (goalkeeper is 1) can be partitioned into defenders, midfielders and forwards so each group's shirt-number sum is divisible by 11. Puzzle 2 notes that early 11×n products are palindromes and asks how many additional palindromic products occur up to 11×99, with 11×56 = 616 given as an example. Puzzle 3 states the alternating-sum divisibility test for 11 and asks for the largest 10-digit number using each digit 0–9 once that is divisible by 11. Eleven is also tied to University Maths Schools in the UK, with nine currently open including King's and Imperial in London, Exeter, Liverpool, Lancaster and Cambridge.
Read at www.theguardian.com
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