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Emma's Dilemma

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Ephraim Greenland


1)        This is all the different arrangements of the name EMMA.

EMMA                EAMM                EMAM

MEMA                MMEA                MAME                

MAEM                AEMM                AMME                

AMEM                MMAE                MEAM

2)        This is all the different arrangements of the name LUCY

LUCY                        LCUY                        LYUC

LUYC                        LCYU                        LYCU        

ULCY                        ULYC                        UCLY                        

UCYL                        UYCL                        UYLC                

CLUY                        CLYU                        CYLU                

CYUL                        YLCU                        YLUC

YULC                        YUCL                        YCLU

YCUL                        CULY                        CUYL

The reason EMMA (a 4 letter name) has only 12 different arrangements LUCY has 24 is because in EMMA there are two of the same letters in the name and so it restricts the possible amount of combinations, however in the name LUCYall the letters in the names are different so you get the maximum amount of combinations.

3)         These are the names that I chose to investigate for different arrangements.  I chose 3 names under each amount of letters.

2 Letter Names

This is all the different arrangements of the name

...read more.


AKTE                        AKET                        AETK

AEKT                        AETK                        AEKT

TKAE                        TKEA                        TAKE                

TAEK                        TEKA                        TEAT

EKAT                        EKTA                        EAKT

EATK                        ETKA                        ETAK

I chose the name KATE because I wanted to see if this would have the same outcome as the names NICK and LUCY.

This is all the different arrangements of the name ROSS.  (I chose the name ROSS because I wondered if it would have the same effect as EMMA did.)

ROSS                        RSSO                        RSOS                

SRSO                        SROS                        SSRO

SOSR                        SORS                        SSOR

ORSS                        OSSR                        OSRS

I chose the name ROSS because I wanted to see if by using a double letter would have the same affect as with EMMA.

My Formula.

My formula for working out how many different combinations a name has is:

2 Letter Names


There are only 2 possible arrangements of a 2 letter name.

MO                        OM

3 Letter Names


JIM                        JMI                        MIJ

IMJ                        IJM                        MJI

4 Letter Names

...read more.


LKIYE                        LKIEY                        LKEYI

LKEIY                        LYKIE                        LYKEI

LYEKI                        LYEIK                        LYIKE

LYIEK                        LIKYE                        LIKEY

LIYKE                        LIYEK                        LIEKY

LIEYK                        LEKYI                        LEKIY

LEYKI                        LEYIK                        LEIYK

LEIKY                        IYKLE                        IYKEL

IYLKE                        IYLEK                        IYEKL

IYELK                        IKYLE                        IKYEL

IKLYE                        IKLEY                        IKELY

IKEYL                        ILKEY                        ILKYE

ILYKE                        ILYEK                        ILEKY

ILEYK                        IEKYL                        IEKLY

IEYLK                        IEYKL                        IELKY

IELYK                        EKYLI                        EKYIL

EKILY                        EKIYL                        EKLIY

EKLYI                        EYKLI                        EYKIL

EYILK                        EYIKL                        EYLKI

EYLIK                        ELKYI                        ELKIY

ELYKI                        ELYIK                        ELKYI

ELKIY                        EIKLY                        EIKLY

EILYK                        EILKY                        EIYKL

My prediction said that there would be 120 different combinations of the name KYLIE.  I proved my theory by making a list of all of the different possible combinations of the name and it came out as 120.


For a 2 letter word:


For a 3 letter word:


For a 4 letter word:


For a 5 letter word:


If there is a double letter in the name then e.g. for a 4 letter word you do 1x2x3x4/2, and if there is 3 letters the same in one name with 5 letters, then you would do 1x2x3x4x5/3 etc…

...read more.

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