¶ 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:
A.
B.
C.
D.
E.
Solution:
Each number is added once per line it is on. Every point is on lines except for , which is on lines. This means:
So:
Since are unique digits from 1 to 6, each digit is represented exactly once, making:
With the equation:
we substitute into it:
which simplifies to:
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions