Looping 2

For this looping trick you start with any two numbers from 0 to 9 and follow this rule: add the two numbers and write down just the digit that is in the ones place. 

For example, start with 8 and 9. Adding them gives you 17. Keep just the 7, which is in the ones place. Now you have 8-9-7. Add the last two numbers, the 9 and the 7. That gives 16; just keep the 6, then you have 8-9-7-6. Keep going, adding the last two numbers in the series each time, keeping only the digit in the ones place. Do this until you get 8 and 9 again. Then the loop starts all over. How many numbers are in the 8-9 loop before it repeats? 

What happens with 2 and 6?

Does the order of the numbers you choose make a difference?

Post your ideas and findings! Remember to write your name at the beginning of your post. 

Looping 1

Start with any number you like and follow these rules. If the number you start with is even, divide it in half. If the number is odd, multiply it by 3, then add 1. Whatever answer you get, apply one of these rules to it again. Do it over and over again - that's the looping part. 

For example, start with 10. It's even, so take half. That gives you 5. That's odd, so multiply it by 3 and add 1: (5x3) +1 = 16. Back to even, so take half and get 8. Half again gives you 1. Since 1 is odd, multiply it by 3 and add 1 to get 4. Half of 4 gives you 2, and half of that gets you back to 1. You're in a loop now and will be forever if you keep at it. 

Try the same procedure with 30 and see what happens. 

Try a few more. What do you notice? Does something happen each time? Write a post to explain what you discovered. Remember to begin each post with your name. 

Poison

Poison is a game for two people. For the first game, use thirteen objects. Players take turns removing one or two objects. Play until all objects have been taken. The last object to be removed is considered to be the poison. Whoever gets stuck taking it loses. What is your winning strategy?

King Arthur's Problem

King Arthur's daughter wanted to marry. She loved maths and created a problem for King Arthur's knights to solve. The knight who solved the problem would prove himself to be logical and brave, therefore worthy to become the lucky husband. The knights were told of the problem in advance and could choose whether or not to compete for the daughter's hand, but they were not told that King Arthur would not actually chop off anyone's head. All of the knights were to gather and be seated at the round table, then King Arthur would point to the knight in the first chair and tell him, "You live." To the next, rather unlucky knight, King Arthur would point and say, "You die." To the third knight he would say, "You live," and to the fourth, "Off with your head!" He would continue doing this around the table, chopping off the head of every other knight, until only one knight remained alive. The remaining knight would marry King Arthur's daughter. Where is the safe seat? Find the safe place to sit with different numbers of knights. Find a pattern so you can predict where to sit no matter how many people are seated in the circle. You need a strategy and method for recording your findings such as, when there are 12 knights, the safe seat is ___; when there are 20 knights, the safe seat is ___. Think about your strategy, then talk to a friend before you begin. You may work with a partner if you wish. Be sure to put both names at the beginning of your post when you share your discoveries.