Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 3.9 AMC 10/12 Find the answer North Macedonia

From the digits $3$ , $7$ , $1$ , $9$ , $0$ and $4$ Mila formed the biggest and the smallest six-digit number using each digit exactly once in each of the two numbers. Then she reduced their difference $9$ times. Which number did she get?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

The biggest six-digit number that can be formed from these digits, using each digit exactly once is $974310$ and the smallest is $103479$ . Their difference is $974310 - 103479 = 870831$ . After Mila reduced their difference $9$ times she obtained the number $870831 : 9 = 96759$ .

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