http://www.geom.uiuc.edu/~addingto/number_bracelets/number_bracelets.html)
Imagine that you have lots of beads, numbered from 0 through 9, as many as you want of each kind.
Here are the rules for making a number bracelet:
- Pick a first and a second bead. They can have the same number.
- To get the third bead, add the numbers on the first and second beads. If the sum is more than 9, just use the last (ones) digit of the sum.
To get the next bead, add the numbers on the last two beads you used, and use only the ones digit. So to get the fourth bead, add the numbers on the second and third beads, and use the ones digit.
Keep going until you get back to the first and second beads, in that order. - How long (or short) a bracelet can you make?
How long is the longest?
How short is the shortest?
How many number bracelets are there?
- How many different starting points?
- How many different bracelets?
Does it necessarily repeat?
Extensions:
Change the mod/cutting number
Change the rule (from Fibonacci to some other sequence)
Why no bracelet of 6?
Why no bracelet of 5, 10, other factors of 60?
What if only use even numbers between 0 and 9?
Prime Number Monopoly
Materials: 2 dice, 5 cards (one for each of the first 5 prime #s) with the following costs and deed contracts:
Prime Number Deed:
Cost:
2 – $250
3 – $167
5 – $100
7 – $71
11 – $45
The owner of this deed
splits the winnings
when another player gets a multiple of:
(prime number here)
Cost:
2 – $250
3 – $167
5 – $100
7 – $71
11 – $45
The owner of this deed
splits the winnings
when another player gets a multiple of:
(prime number here)
Game: Roll two dice and can choose the amount of either number formed by those two digits. Can buy prime numbers. Then whenever another player chooses a number that is a multiple of your number, they split the $ with you.
Goal: Get as much money as possible (there will be times when it will be to your advantage to choose the smaller number). Play for a set amount of time, clearly stated in advance.
Questions:
How did I work out the pricing?
What’s the best prime real estate buy?
I saw Mary O'Keefe at the Great Circles Workshop. She's great! What's the conference you're at?
ReplyDeleteThis monopoly game looks interesting, but I might have to ask a few questions to understand it. Too tired now...