The largest and smallest 9-digit numbers divisible by 11
Using nine of the ten digits 0–9 (each used at most once, with exactly one digit left out), what is the largest number you can form that divides evenly by 11? Using the same rule, what is the smallest such number?
Reveal the answer
Largest: 987,652,413 (leaving out 0). Smallest: 102,347,586 (leaving out 9). Henry Dudeney set this as 'The Mystic Eleven,' puzzle no. 93 in Amusements in Mathematics (1917), solved with the rule that a number is divisible by 11 when the difference between its odd-position and even-position digit sums is itself a multiple of 11.
— Henry Ernest Dudeney, Amusements in Mathematics — 1917, puzzle no. 93
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