GCSE Math Coursework: Triminoes

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GCSE Math Coursework

INTRODUCTION

Triminoes is a game similar to dominoes. The game is played using triangular pieces of card. Each card has three numbers on it. Instead of drawing the triangles I will write the three numbers in brackets below.

E.g.

(000)                (001)                (002)                (011)                (012)

(022)                (111)                (112)                (122)                (222)

The aim of this investigation will be to:

  1. Investigate the relationship between the number of Triminoe cards in a set and the largest number used in a set.
  2. Investigate the relationship between the sum of all numbers on a set of Triminoe cards and the largest number used on the cards.

PLANNING

These are some of the formulas I will be using in order to complete the tasks:

f (n) =an+b                                 (Linear equation)

f (n) =an2+bn+c                         (Quadratic equation)

f (n) =an3+bn2+cn+d                 (Cubic equation)

f (n) =an4+bn3+cn2+dn+e         (Quartic equation)

METHOD

  1. First I am going to the number 0 and find out how much different possibilities I can make with the one number, this is obviously one.
  2. I will then try two numbers 0 and 1 and find out how much different possibilities I can make with the two numbers.
  3. I will continue to do this until I feel I have used enough numbers.
  4. On each set of data I will record the largest number used, the sum of all the cards added together, and the number of cards used.
  5. I will then make a results table.
  6. I will collect the data from each group and place it together then I will find out whether the equation is a linear, quadratic, cubic or quartic.
  7. By replacing the correct numbers with the correct letters I will find out the formula.
  8. I will then write down the formula for each set of sequence.

Using number 0

(000)





Using numbers 0 and 1

(000)                (001)

(011)                (111)






Using numbers 0, 1 and 2

(000)                (001)                (002)                (011)                (012)

(022)                (111)                (112)                (122)                (222)




Using numbers 0, 1, 2 and 3

(000)                (001)                (002)                (003)                (011)

(012)                (013)                (022)                (023)                (033)

(111)                (112)                (113)                (122)                (123)

(133)                (222)                (223)                (233)                (333)





Using numbers 0, 1, 2, 3 and 4

(000)                (001)                (002)                (003)                (004)        

(011)                 (012)                (013)                (014)                (022)                

Join now!

(023)                 (024)                (033)                (034)                (044)

(111)                (112)                (113)                (114)                (122)        

(123)                (124)                (133)                (134)                (144)

(222)                (223)                (224)                (233)                (234)

(244)                (333)                (334)                (344)                (444)





Using numbers 0, 1, 2, 3, 4 and 5

(000)                (001)                (002)                (003)                (004)                (005)

(011)                (012)                (013)                (014)                (015)                (022)

(023)                (024)                (025)                (033)                (034)                (035)

(044)                (045)                (055)                (111)                (112)                (113)

(114)                (115)                (122)                (123)                (124)                (125)

(133)                (134)                (135)                (144)                (145)                (155)

(222)                (223)                (224)                (225)                (233)                (234)

(235)                (244)                (245)                (255)                (333)                (334)

(335)                (344)                (345)                (355)                (444)                (445)

(455)                (555)





Using numbers 0, 1, 2, 3, 4, 5 and 6

(000)                (001)                (002)                (003)                (004)                (005)

(006)                (011)                (012)                (013)                (014)                (015)

(016)                (022)                (023)                (024)                (025)                (026)

(033)                (034)                (035)                (036)                (044)                (045)

(046)                (055)                (056)                (066)                (111)                (112)

(113)                (114)                (115)                (116)                (122)                (123)

(124)                (125)                (126)                (133)                (134)                (135)

(136)                (144)                (145)                (146)                (155)                (156)

(166)                (222)                (223)                (224)                (225)                (226)

(233)                (234)                (235)                (236)                (244)                (245)

(246)                (255)                (256)                (266)                (333)                (334)

(335)                (336)                (344)                (345)                (346)                (355)

(356)                (366)                (444)                (445)                (446)                (455)

(456)                (466)                (555)                (556)                (566)                (666)




RESULTS TABLE

Largest Number

1                2                3                4                5                6

        +1        +1        +1                +1        +1

Linear Equation

FORMULA

f (n) =an + b

f (n) = 1n + 0

        

Sum of all numbers

6        30        90         210                     420              756

...

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