Emma's Dilemma

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Emma's Dilemma

In my investigation I will investigate the number of different

combinations a word can be put in. For example the word… Tim.

The letters in this word can be mixed up to show all the possible

variations of combinations the letters can be put in. So a variation

of the name Tim would be… Mit.

E.g. TIM, ITM, MIT,

TMI, ITM, MTI. …this shows all the possible combinations the letters

can be put

into. A total of 6 different combinations can be achieved.

I will begin by investigating the name LUCY. I will work out all the

possible letter combinations that can be produced from this name. I

have chosen this name because it has no letters the same and I first

intend to investigate words with no letters repeated before perhaps

moving on to that situation.

LUCY

LUYC

LYCU

LYUC

LCYU

LCUY

YUCL

YULC

YLCL

YLUC

YCUL

YCLU

CLUY

CLYU

CULY

CUYL

CYLU

CYUL

ULCY

ULCY

UCYL

UCLY

UYLC

UYCL

Total = 24 variations.

I will try the same with a 3-letter name to see if there is some sort

of pattern.

TIM

TMI

IMT

ITM

MTI

MIT

Total = 6 variations

I can not yet see any sort of connection yet other than they are both

even numbers, I will do the same thing with a 2-letter name.

TO

OT

Total = 2 different arrangements.

I will now draw a table to show my results this may help me find

connection more easily because the links will be more visible.

Table of Results

================

Number of Letters

Number of Different Arrangements

2

2

3

6

4

24

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