Won't this be better posed as a problem instead of as a note?
–
Calvin Lin
Staff
·
1 year, 7 months ago

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In the example,
\[6+2=8\\2+7=9\\7+6=13\]
This suggests that the rule is that:
\[\text{The sum of the numbers on the endpoints of the line segments is the number written in the square present on that line}\]
The rest is just simple,

Let (moving right from the topmost ? clockwise) the 3 ?s in each of the 3 questions be denoted \(x_n ,y_n,z_n\) respectively(\(n\) being the number of the question) .Then we have the set of equations:
\[\text{For the 1st}
\begin{cases}x_1+y_1=10\\y_1+z_1=4\\z_1+x_1=12\end{cases}\]
\[\text{For the 2nd}
\begin{cases}x_2+y_2=13\\y_2+z_2=7\\z_2+x_2=12\end{cases}\]
\[\text{For the 3rd}
\begin{cases}x_3+y_3=9\\y_3+z_3=5\\z_3+x_3=14\end{cases}\]
Simply solving these sets of equations gives the answer.
–
Abdur Rehman Zahid
·
1 year, 7 months ago

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(9,3,1),(9,3,4),(9,5,0)
–
Venture Hi
·
1 year, 7 months ago

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TopNewestWon't this be better posed as a problem instead of as a note? – Calvin Lin Staff · 1 year, 7 months ago

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In the example, \[6+2=8\\2+7=9\\7+6=13\] This suggests that the rule is that: \[\text{The sum of the numbers on the endpoints of the line segments is the number written in the square present on that line}\] The rest is just simple,

Let (moving right from the topmost ? clockwise) the 3 ?s in each of the 3 questions be denoted \(x_n ,y_n,z_n\) respectively(\(n\) being the number of the question) .Then we have the set of equations: \[\text{For the 1st} \begin{cases}x_1+y_1=10\\y_1+z_1=4\\z_1+x_1=12\end{cases}\] \[\text{For the 2nd} \begin{cases}x_2+y_2=13\\y_2+z_2=7\\z_2+x_2=12\end{cases}\] \[\text{For the 3rd} \begin{cases}x_3+y_3=9\\y_3+z_3=5\\z_3+x_3=14\end{cases}\] Simply solving these sets of equations gives the answer. – Abdur Rehman Zahid · 1 year, 7 months ago

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(9,3,1),(9,3,4),(9,5,0) – Venture Hi · 1 year, 7 months ago

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