¶ 2020 AMC8 Problem 16
Problem:
Suppose Each of the points and in the figure below represents a different digit from to . Each of the five lines shown passes through some of these points. The digits along each line are added to produce five sums, one for each line. The total of the five sums is . What is the digit represented by
Answer Choices:
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E.
Solution:
The total of the five sum is
which equals . The expression equals , the sum of the digits from to , so . Therefore .
Note that every point lies on exactly two lines except for , which lies on three lines. Because the sum of the digits from to is , this gives a total sum of . Therefore .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions