An arithmagon is a shape with numbers
and a rule attached to it.
What are the rules?
Aim
Our aim is to investigate arithmagon solutions.
We will look for patterns and relationships in the
numbers.
This will help us to answer two questions.
What are those questions?
Using the square arithmagons
blank sheet, find a solution for:
E = 12 F = 9 G = 4 H = 1
What is your solution?
Can you find a different one?
How many solutions are there
altogether?
Record your results in a table:
Given E = 12
Found:
A
F=9
B
G=4
C
D
H=1
Now try these:
1. E = 1
2. E = 7
3. E = 6
4. E = 17
5. E = 8
F=7
F=3
F=8
F = 15
F=6
G=4
G = 13
G = 11
G = 13
G=9
H = 10
H=9
H = 13
H = 11
H=5
In each case, try to make sure that you
have all the possible solutions
Key questions
 Have you got a system for working out your
solution?
 Are there any rules about how many solutions
there will be?
 What other patterns or rules have you
discovered?
 Are there any sets of numbers (E, F, G, H) that do
not work. If so, why do you think this is?
Tip 1
Look at the number of solutions for any one
square arithmagon.
Compare it with the smallest number in the
squares.
How does it compare?
Is this always true?
Tip 2
Add up the numbers opposite one another in the
squares.
Eg E + H and F +G
What do you notice?
Tip 3
Add up E + F + G + H
Add up A + B + C + D
What do you notice?
Tip 4
Why does problem 6 not work?
Can you find another combination which does
not work?
Analysis of Results
• How can you predict the number of solutions
there will be?
• How do you know if an arithmagon is
solvable?
• Is there a relationship between the numbers
in squares and circles?
• Consider patterns of odd and even numbers,
opposite numbers, diagonally opposite
numbers.