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Vandaag is het 19 November 2018

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Bank account number - math puzzle

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Today, John has to transfer 50 euro to the bank account of a Dutch friend. He has written down the account number on a piece paper. But since he had forgotten to take out the paper from his trousers when he put them in the washing machine, one digit of the bank account number became unreadable. The note says: 3170?4847. The friend of John is climbing the Mount Everest at the moment, so it is impossible for John to call his friend. Suddenly he remembers that a for a valid Dutch bank account number it holds that the first digit times 9 + the second digit times 8 + the third digit times 7 + ...... + the nineth digit times 1 should be divisible by 11. John thinks for a moment and finds the correct number. What is it?

Explanation

Let us call the unreadable number x. The bank account number is hence 3170x4847.
The first digit times 9 + the second digit times 8 + the third digit times 7 + ...... + the nineth digit times 1 should be divisible by 11. So 27 + 8 + 49 + 0 + 5*x + 16 + 24 + 8 + 7 should be divisible by 11, in other words 139 + 5 * x should be divisible by 11. Since 132 = 11*12 it follows that 7 + 5 * x should be divisible by 11. That only works if x = 3.
Hence the correct bank account number is 317034847.