2020 AMC 8 Problems/Problem 16
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
Solution 1
We can form the following expressions for the sum along each line: Adding these together, we must have , i.e. . Since are unique integers between and , we obtain (where the order doesn't matter as addition is commutative), so our equation simplifies to . This means .
Solution 2 (similar to Solution 1)
We can see that . Combining like terms, we get . Since and are all distinct integers ranging from 1 to 6, they must sum up to , so .
Video Solution
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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