Emma's Dilemma

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Emma’s Dilemma

        For our maths coursework we had to investigate the number of different word arrangements possible for names. The names (or letter arrangements) I started off with had letters that were only used once n each name and were not repeated, like “Lucy”. As I continued experimenting with the different arrangements, I began to use words with letters repeating, such as “Emma”. My goal was to find formulas that worked for the different arrangements.

        I started off by working out the number of different arrangements in the name “Emma”. I shall now display the different arrangements of “Emma” that I found:

EMMA

EMAM

EAMM

MMEA

MMAE

MAME

MAEM

MEAM

MEMA

AMME

AEMM

AMEM

        Here are the different letter arrangements for “Lucy”:

LUCY          ULCY          CLUY          YLUC

LUYC          ULYC          CLYU          YLCU

LCUY          UCLY          CULY          YULC

LCYU          UCYL          CUYL          YUCL

LYUC          UYLC          CYLU          YCLU

LYCU          UYCL          CYUL          YCUL

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        I will now go through the different arrangements for names or word arrangements that do not have any repeats and are one, two, three, four and five letters long:

A

JO   OJ

MAX   MXA   AMX

AXM   XMA   XAM

MIKE   MIEK   MKIE   MKEI   MEIK   MEKI

IMKE   IMEK   IKME   IKEM   IEMK   IEKM

KMIE   KMEI   KIME   KIEM   KEMI   KEIM

EMIK   EMKI   EIMK   EIKM   EKMI   EKIM

MINTY          MNITY   ...

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