Maths Olympiad Prep

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Combinatorics Difficulty 4.0 AMC 10/12 Find the answer Philippines

Problem:
What is the sum of all four-digit numbers that each use the digits 2,4,62, 4, 6, and 88 exactly once?

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

Solution

Solution:
Every digit appears in each decimal place exactly 66 times. Therefore, the sum is 6(2+4+6+8)1111=133,3206 \cdot (2+4+6+8) \cdot 1111 = 133,320.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.