×

# Arithmagons

Can, Can, Describe

Note by Llewellyn Sterling
2 years ago

Sort by:

Won't this be better posed as a problem instead of as a note? Staff · 2 years ago

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. · 2 years ago