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Explore the Back-StoryTry this beautiful Problem based on line from AMC 8 2020.

Each of the points $A, B, C, D, E$, and $F$ in the figure below represents a different digit from 1 to 6 . 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 47 . What is the digit represented by $B$ ?

- 1
- 2
- 3
- 4
- 5

Lines

Combination

Digit Find

AMC 8 2020 Problem 16

5

Try to find the sumes alongs lines

\begin{aligned}

&A+B+C \

&A+E+F \

&C+D+E \

&B+D \

&B+F

\end{aligned}

Adding The sums all together, we will have $2 A+3 B+2 C+2 D+2 E+2 F=47$, i.e. $2(A+B+C+D+E+F)+B=47$

So we will have $42+B=47$, now we need solve this equation for B.

Try this beautiful Problem based on line from AMC 8 2020.

Each of the points $A, B, C, D, E$, and $F$ in the figure below represents a different digit from 1 to 6 . 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 47 . What is the digit represented by $B$ ?

- 1
- 2
- 3
- 4
- 5

Lines

Combination

Digit Find

AMC 8 2020 Problem 16

5

Try to find the sumes alongs lines

\begin{aligned}

&A+B+C \

&A+E+F \

&C+D+E \

&B+D \

&B+F

\end{aligned}

Adding The sums all together, we will have $2 A+3 B+2 C+2 D+2 E+2 F=47$, i.e. $2(A+B+C+D+E+F)+B=47$

So we will have $42+B=47$, now we need solve this equation for B.

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