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Emma’s Dilemma.

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Introduction

Emma’s Dilemma

Part 1

Introduction

In this investigation, I am going to find out the different arrangements of the letters of the name LUCY.

Here are the possibilities for the name LUCY

LUCY UYCL YCLU CULY

LCYU UCLY YLCU CYLU

LYCU ULUC YULC CLYC

LCUY ULUY YLUC CUYL

LUYC UCLY YCUL CYUL

LYUC UYLC YULC CLUY

First of all I took the letter L from the name LUCY then wrote the second letter being U and after the two other possibilities being C and Y. Then after I used the same letter L, wrote the second letter down being C and wrote the two possibilities again being U and Y. I took another letter which I used that to be the second letter, keeping the first letter the same in till I have found the rest of the possibilities in the letter.

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Middle

I am now going to try to find a pattern in the possibilities of combinations of different letters.

a) Firstly with one letter.

A

There is one permutation with one letter.

b) With two letters.

AB BA

There are two possibilities with two different letters.

c) With three letters.

ABC BAC CBA

ACB BCA CAB

There are six permutations with three different letters.

d) With four letters.

ABCD BACD CABD DABC

ABDC BADC CADB DACB

ACBD BCAD CBAC DBAC

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Conclusion

pan>

1

2

6

24

?

1! = 1 x 1 =1

2! = 1 x 2 =2

3! = 1 x 2 x 3 =6

4! =1 x 2 x 3 x 4 =24

From this table I predict that with five letters there will be 120 permutations.

5! = 1 x 2 x 3 x 4 x 5 = 120

e) With five letters.

ABCDE BACDE CABDE DABCE EABCD

ABCED BACED CABED DABEC EABDC

ABDCE BADCE CADBE DACBE EACBD

ABDEC BADEC CADEB DACEB EACDB

ABECD BAECD CAEBD DAEBC EADBC

ABEDC BAEDC CAEDB DAECB EADCB

ACBDE BCADE CBADE DBACE EBACD

ACBED BCAED CBAED DBAEC EBADC

ACDBE BCDAE CBDAE DBCAE EBCAD

ACDEB BCDEA CBDEA DBCEA EBCDA

ACEBD BCEAD CBEAD DBEAC EBDAC

ACEDB BCEDA CBEDA DBECA EBDCA

ADBCE BDACE CDABE DCABE ECABD

ADBEC BDAEC CDAEB DCAEB ECADB

ADCBE BDCAE CDBAE DCBAE ECBAD

ADCEB BDCEA CDBEA DCBEA ECBDA

ADEBC BDEAC CDEAB DCEAB ECDAB

ADECB BDECA CDEBA DCEBA ECDBA

AEBCD BEACD CEABD DEABC EDABC

AEBDC BEADC CEADB DEACB EDACB

AECBD BECAD CEBAD DEBAC EDBAC

AECDB BECDA CEBDA DEBCA EDBCA

AEDBC BEDAC CEDAB DECAB EDCAB

AEDCB BEDCA CEDBA DECBA EDCBA

Ali Khizar Set 3

Maths Coursework

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