This is all the different arrangements of the name BEN
BEN NEB BNE
ENB EBN NBE
This is all the different arrangements of the name ANN. (I chose Ann because it had 2 of the same letters in its name, and to see what effect it had on the amount of different arrangements.)
ANN NAN NNA
4 Letter Names
This is all the different arrangements of the name NICK
NICK NCIK NKIC
NIKC NCKI NKCI
INCK INKC ICNK
ICKN IKCN IKNC
CNIK CNKI CKNI
CKIN CINK CIKN
KNCI KNIC KINC
KICN KCNI KCIN
I chose the name NICK because I wanted to see if it had the same outcome as the name LUCY and it did.
This is all the different arrangements of the name KATE
KATE KTAE KAET
KETA KEAT KTEA
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
1x2=2
There are only 2 possible arrangements of a 2 letter name.
MO OM
3 Letter Names
1x2x3=6
JIM JMI MIJ
IMJ IJM MJI
4 Letter Names
1x2x3x4=24
NICK NCIK NKIC
NIKC NCKI NKCI
INCK INKC ICNK
ICKN IKCN IKNC
CNIK CNKI CKNI
CKIN CINK CIKN
KNCI KNIC KINC
KICN KCNI KCIN
For a name that has 2 letters that are the same, all you have to do to find the amount of different arrangements is do the formula then divide it by 2.
Like EMMA
1x2x3x4/2=12
EMMA EAMM EMAM
MEMA MMEA MAME
MAEM AEMM AMME
AMEM MMAE MEAM
So for a 5 letter name I predict that I will find 120 different combinations.
I will do the name KYLIE
KYLIE KYLEI KYELI
KYEIL KYIEL KYILE
KLYIE KLYEI KLEYI
KLEIY KLIEY KLIYE
KILYE KILEY KIELY
KIEYL KIYLE KIYEL
KEYLI KEYIL KELYI
KEIYL KEILY KEILY
YKLIE KELIY YKLEI
YKELI YKEIL EIYLK
YKILE YLKIE YLKEI
YLIKE YLIEK YLEKI
YLEIK YIKLE YIKEL
YILKE YILEK YIEKL
YIELK YEKLI YEKIL
YELKI YELIK YEILK
YEILK LKYIE LKYEI
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.
MY FORMULA
For a 2 letter word:
1x2
For a 3 letter word:
1x2x3
For a 4 letter word:
1x2x3x4
For a 5 letter word:
1x2x3x4x5
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…
