Why Beckham wears 23

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Why Beckham wears 23
By Sarah Bonnell School
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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.

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Prime Hopscotch
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Prime hopscotch
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 youll 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 cant go anywhere. Good
luck in playing.
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Continued...
REMEMBER When your playing this it will really
brush you up on your prime numbers. If you press
a none prime number you lose!!
If you want to win land on the numbers
7,13,17,19,23,89,113
Continued..
A little sneaky Stratergy!!
No matter if your jump is 1-13
If you get to 113 the
computer has lost!!
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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.
I concluded that...
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Thanks for watching the hopscotch presentation!
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STARS
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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

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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

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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 wasnt 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

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Cicadas
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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 cicadas 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.
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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 .

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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 .
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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?

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Cicada
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.
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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 wouldnt appear in the forest when the
  predator would.

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Fantasy Football
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Aim of the Game
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.
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What we did...
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
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Newcastle
2,2,2,2,2,2,2
2-2
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Solution
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
www.musicoftheprimes.com/01intro.htm. We hope
you have learnt from this presentation.
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By Sarah Bonnell School