GCSE Maths Project – “Emma’s Dilemma”

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Murray Goodwin GCSE Maths Project - "Emma's Dilemma"

Part 1:

Ways of arranging EMMA's name:

EMMA

MEMA

MMAE

AMME

EMAM

MEAM

MAEM

AMEM

EAMM

MMEA

MAME

AEMM

For each new beginning letter, there are 3 different possible combinations.

There are a total of 12 possible different combinations.

Part 2:

Ways of arranging LUCY's name:

LUCY

ULCY

CULY

YUCL

LUYC

ULYC

CUYL

YULC

LCUY

UCLY

CLUY

YCUL

LCYU

UCYL

CLYU

YCLU

LYUC

UYLC

CYLU

YLUC

LYCU

UYCL

CYUL

YLCU

For each new beginning letter, there are 6 different possible combinations.

There are a total of 24 possible different combinations.

Summary of Parts 1 and 2:

EMMA and LUCY both have the same number of letters in their names, however LUCY has twice as many different letter combinations. This is because EMMA's name has a repeating letter (in this case the letter "M" is repeated) whereas the letters in LUCY's name are all different.