Question

# What if more than two digits are interchanged? Will the difference stiU be divisible by $9$? Illustrate your answer

Solution

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Recall that we can figure out if the number is divisible by $9$ if the sum of its digits is also divisible by 9. Since juggling the digit placements will not affect the sum of all the digits, hence, interchanging any digits should not affect the divisibility of its number.