Emma's Dilemma

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Emma's Dilemma

In my investigation I am going to investigate the number of different

arrangements of letters for names and words and try to find a formula

that can be used to predict this.

For example: TOM is one arrangement

and OTM is another arrangement

First, I am going to investigate the number of different arrangements

of letters for the name LUCY (a 4-letter name, where all the letters

are different).

LUCY ULCY CLUY YLUC

LUYC ULYC CLYU YLCU

LCUY UCLY CULY YULC

LCYU UCYL CUYL YUCL

LYUC UYLC CYLU YCLU

LYCU UYCL CYUL YCUL

There are 4 different letters and 24 different arrangements.

Once I have investigated the number of different arrangements for one

4-letter name/word where all the letters are different, I do not need

to try any more. If I tried the name DAVE for example, there would

still be 24 different arrangements. I could substitute the L in LUCY

for the D in DAVE, the U for A, the C for V, and the Y for E; and

would therefore end up with the same result. The same is true for

names/words with 3 letters or 5 letters, etc. As long as the number of

letters and the number of different letters are the same, the number

of different arrangements will be the same.

Now I will investigate a 3-letter name where all the letters are

different.

SAM ASM MSA

SMA AMS MAS

There are 6 different arrangements.

Now I will investigate a 2-letter name where all the letters are

different.

JO OJ

There are 2 different arrangements.

Now I am going to investigate a 5-letter name where all the letters

are different.

KATIE AKTIE TKAIE IKATE EKATI

KATEI AKTEI TKAEI IKAET EKAIT

KAITE AKITE TKIAE IKTAE EKTAI

KAIET AKIET TKIEA IKTEA EKTIA

KAETI AKETI TKEAI IKEAT EKIAT

KAEIT AKEIT TKEIA IKETA EKITA

KTAIE ATKIE TAKIE IAKTE EAKTI

KTAEI ATKEI TAKEI IAKET EAKIT

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