## Excel in math and science

### Master concepts by solving fun, challenging problems.

## It's hard to learn from lectures and videos

### Learn more effectively through short, conceptual quizzes.

## Our wiki is made for math and science

###
Master advanced concepts through explanations,

examples, and problems from the community.

## Used and loved by 4 million people

###
Learn from a vibrant community of students and enthusiasts,

including olympiad champions, researchers, and professionals.

## Comments

Sort by:

TopNewestWon't this be better posed as a problem instead of as a note?

Log in to reply

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.

Log in to reply

(9,3,1),(9,3,4),(9,5,0)

Log in to reply