# 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) =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)

(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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