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Information about PrimesSarahBonnell

Published on December 30, 2007

Author: cooper


Why Beckham wears 23:  Why Beckham wears 23 By Sarah Bonnell School Introduction:  Introduction We are students from Sarah Bonnell School. We have been looking at how Prime Numbers come into everyday life. For example:“ Why did David Beckham wear the number 23 on his shirt for Real Madrid?” But first of all we have been looking at prime games and have been working out different methods and strategies of how to win. This presentation tells you all about the games we have been looking at. We hope you enjoy this presentation. Slide4:  In this presentation we will be talking about the game prime hopscotch. This is a game all about prime and seeing if you can use your knowledge of them to beat the computer and to not get stuck, but you’ll see all about that later. What do you do? .In this game you play against the computer, jumping on prime numbers. In this game you can only land on primes and when you get stuck you lose. Try and beat the computer by immobilising it so it can’t go anywhere. Good luck in playing. Slide5:  If you want to win land on the numbers 7,13,17,19,23,89,113 No matter if your jump is 1-13 If you get to 113 the computer has lost!! REMEMBER When your playing this it will really brush you up on your prime numbers. If you press a none prime number you lose!! Continued….. Slide6:  As I played the game, I found out that there were certain prime numbers that you had to land on first to win. These numbers are: 7, 13, 17, 19, 23, 89, 113. If the computer landed on 7 first when your maximum jump was 2 or 3, you would lose because the next available prime number (11) is 4 jumps away. When your maximum jump is 4/5/6, it is best to land on 23 because the next prime number is at 31, which is 7 jumps away. The next prime number that you have to land on first, if your Maximum jump is 7/8 is 89 because the next prime numbered is 97. Stars:  Stars One of the games that we looked at was Stars. To play, you have to move around the points in a circle in different step lengths. The number of points in a circle and the step length determines whether you hit all the points or not. If you have 6 points in the circle, for example, you can move around in step lengths of 1, 2, 3, 4 and 5. If you move around the circle in steps of 1, you hit all the points If you move around in steps of 2, you miss some points If you move around in steps of 3, you miss some points You can experiment how many points you hit with different number of points in a circle and different step lengths Stars:  Stars When you have 8 points in a circle, stepping by 1 hits all the points Stepping by 2 misses some points Stepping by 3 hits all the points Stepping by 4 misses some points Stepping by 5 hits all the points Stepping by 6 misses some points Stepping by 7 hits all the points Stars:  Stars The solution: After having played the game several times, I noticed that when the number of points in a circle was prime, all the points were hit every time But then what about when the number of points in the circle wasn’t prime? After playing the game more times, I realised that all the points were hit if the Highest Common Factor between the number of points and the step length was 1 Slide12:  Cicadas Slide13:  Cicada Rules: You are a cicada . You hide in the ground for C years, then appear for six weeks: you eat, mate and party, shrieking away so loud that the noise in the forest makes a disco sound like a library. Then after laying your eggs for the next generation of partying cicadas, you die. But there is a predator who ruins the party. The predator only appears every P years. Choose a predator. The cicada’s main predators are the ‘cicada eater’ wasp , and a certain fungus . Choose a number between 5 and 10. This is the life cycle of the predator. Choose a cicada life cycle between 10 and 20. How often do the cicadas and the predators appear in the forest in the same year? This is bad news for cicadas, but good news for predators. Cicada:  Cicada I played this game many times, with many choices and combinations of numbers for the life cycle of Cicada and the life cycle for the Predator . Cicada:  Cicada The 6 next slides contain tables which show all the numbers that I chose for the life cycle of cicada and the life cycle of predator for a 100 years. It also shows the score out of a 100, which is decided by how often the cicada and predator appear in the forest together. When they appear together the predator eats the cicada, which reduces the score. The higher the score the better choice of life cycle year for the cicada. The lower the score, the better choice for the predator . Cicada:  Cicada Task: If you are a cicada, what are your best choices for C? If you are a predator, what are your best choices for P? Once you are familiar with the game, think about strategy. How can the cicadas maximise their chances of not meeting predators? How can the predators maximise their chances of getting their prey? Slide23:  After playing the game with the combinations of all the different numbers, I figured that if the life cycle year of cicada is a multiple of the life cycle year of the predator, than the entire cicada die, and the player scores 0. As every time the cicada appears in the forest, the predator is there. So these type of choices of numbers are best for the predator , because the predator is always there to eat the cicada when they appear to party. Life cycle 5 is also a good choice for the predator , as by choosing this life cycle, the predator appears in the forest at the same time as the cicada, at least once, no matter what life cycle the cicada chooses between 10 and 20. Cicada Cicada:  Cicada I also found out that the life cycle years which are primes are the best choices for the cicada . Especially life cycle 19 and 17, except when the life cycle year of the predator is 5. Cicadas never appear in the forest at the same time as the predator, by choosing 19 or 17 as a life cycle (except if the life cycle of the predator is 5). When the life cycle of the predator is 7, the cicada can choose from life cycle 15 up to 20, which would be a really good choice, as the cicada wouldn’t appear in the forest when the predator would. Slide26:  The objective of this Fantasy Football is to beat the opposing team using various methods and techniques involving prime numbers. Using different ranges of prime numbers, we had to find the correct combination of prime numbers of the winning team. Slide27:  We experimented with a different ranges of prime numbers and searched for the winning team. We played the game many times and recorded our results in the following table… Slide28:  2,2,2,2,2,2,2 Newcastle 2-2 Slide29:  We discovered that choosing low prime numbers helped to win the game. The game is very delightful and we had fun playing it. If you would like to play this game, go to: We hope you have learnt from this presentation. Slide30:  By Sarah Bonnell School

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