NRICH: Arithmagons
NRICH: Arithmagons
An arithmagon is a polygon with numbers at its vertices which determine the numbers written on its edges.
Check you understand how the values at the vertices determine the values on the edges in the arithmagons generated by the interactivity:
8
5
6
If you are given the values on the edges, can you find a way to work out what values belong at the vertices?
Use the interactivity below to test out your strategies.
There are four different challenge levels to try.
Level 1
Level 2
Level 3
Level 4
26
28
16
Once you are confident that you can work out the values at the vertices efficiently, here are some questions you might like to consider:
- Can you describe a strategy to work out the values at the vertices irrespective of the values given for the edges?
- By looking at the numbers on the edges, how can you predict whether the numbers at the vertices will all be positive?
- By looking at the numbers on the edges, how can you predict whether the numbers at the vertices will all be whole numbers?
- What happens to the numbers at the vertices if you increase one or more of the numbers on the edges by 1? By 2? … By n?
- What relationships can you find in square arithmagons? Or pentagonal arithmagons?
A poster of this resource is available here.
NRICH (University of Cambridge)
Math Topics
Addition & Subtraction
Middle School, High School
6th Grade, 7th Grade, 8th Grade, 9th Grade, 10th Grade, 11th Grade
What are you looking for?
Organization
NRICH (University of Cambridge)
Website URL
Type of Resource
Online Game
Assigned Categories
Resource k12
NRICH: Arithmagons
An arithmagon is a polygon with numbers at its vertices which determine the numbers written on its edges.
Check you understand how the values at the vertices determine the values on the edges in the arithmagons generated by the interactivity:
8
5
6
If you are given the values on the edges, can you find a way to work out what values belong at the vertices?
Use the interactivity below to test out your strategies.
There are four different challenge levels to try.
Level 1
Level 2
Level 3
Level 4
26
28
16
Once you are confident that you can work out the values at the vertices efficiently, here are some questions you might like to consider:
- Can you describe a strategy to work out the values at the vertices irrespective of the values given for the edges?
- By looking at the numbers on the edges, how can you predict whether the numbers at the vertices will all be positive?
- By looking at the numbers on the edges, how can you predict whether the numbers at the vertices will all be whole numbers?
- What happens to the numbers at the vertices if you increase one or more of the numbers on the edges by 1? By 2? … By n?
- What relationships can you find in square arithmagons? Or pentagonal arithmagons?
A poster of this resource is available here.
NRICH (University of Cambridge)
Math Topics
Addition & Subtraction
Middle School, High School
6th Grade, 7th Grade, 8th Grade, 9th Grade, 10th Grade, 11th Grade
What are you looking for?
Organization
NRICH (University of Cambridge)
Website URL
Type of Resource
Online Game