# Arithmagons

Can, Can, Describe

Note by Llewellyn Sterling
3 years, 2 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

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

Staff - 3 years, 2 months 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.

- 3 years, 2 months ago

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

- 3 years, 2 months ago