Goals
Explore Frobenius number for the simple 2 number case.
Look for patterns in calculating the number, and the value of the highest number.
What to Do
Review the different coins used in currencies around the world
Create a new (martian) currency using only 2 coins
For example, if the coins are 4c and 7c what values can not be made?
1,2,3,5,6 are trivial
what other values are not possible (9,10,13,17)
go through numbers one by from 10-25 to explore this.
Can we be sure there are no more?
Pick 2 number between 3 and 9 and and find the highest value that can not be made with these 2 coins
be careful not to pick 2 numbers with a common factor and these will go on for ever.
Draw a table to help calculate the missing numbers
e.g. for numbers 4 and 5
It can be seen from this table that the missing numbers are 1,2,3,6,7,11
Homework
Complete the table above for the 2 numbers you selected.
What is the highest number that can not be made with your 2 coins
Bonus: What is the formula between the 2 coin numbers and the highest number that can not be made. Try some more number pairs and look for a pattern.
From our examples we have seen:
Inspiration