Emma's Dilemma.

Emma's Dilemma In this investigation I am going to investigate the number of different arrangements of letters in a word. I will firstly see the number of arrangements of the letters of Emma's name. ARRANGEMENTS FOR EMMA ) EMMA 2) EMAM 3) EAMM 4) AEMM 5) AMEM 6) AMME 7) MMAE 8)MMEA 9) MEAM 10) MAEM 11) MAME 12) MEMA I have found that there are 12 different arrangements. In each word there are total of 4 letters and 2 of them are the same, 'M' which is repeated. Now I shall see how many different arrangements there are in the name Lucy ARRANGEMENTS FOR LUCY ) LUCY 2) LUYC 3) LYUC 4) LYCU 5) LCUY 6) LCYU 7) ULYC 8) ULCY 9) UYCL 10) UYLC 11) UCLY 12) UCYL 13) CLUY 14) CLYU 15) CYUL 16) CYLU 17) CULY 18) CUYL 19) YUCL 20) YULC 21) YLCU 22) YLUC 23) YCUL 24)YCLU There are 24 different arrangements possibilities in this arrangement of 4 letters that are all different, which is twice as many arrangements than EMMA. I shall now investigate on different words, which have different number of letters. I will start by using the word 'JO' ARRANGEMENTS FOR JO ) JO 2) OJ There are two arrangements for this 2-lettered name. I will now investigate the number of arrangements for 'JIM' which is a 3 lettered word ARRNAGEMENTS FOR JIM ) JIM 2) JMI 3) IJM 4) IMJ 5) MJI 6) MIJ There are 6 arrangements for this 3-lettered name, which is triple the number of arrangements

  • Word count: 3131
  • Level: GCSE
  • Subject: Maths
Access this essay

Emma's Dilemma

) Investigate the number of the different arrangements of the letters of EMMA 's name. EMMA* There is 18 different arrangements EMAM of the letters of EMMA, but 6 of EAMM them are the same so there are 12 MEMA different arrangements of the letter MEAM EMMA. MAEM In EMMA, M is duplicated MAME because of this we have 12 MMAE duplicated arrangements in our MMEA list. AMME EMMA AMEM EMAM AEMM EAMM EMMA* MAEM EAMM MAME MMAE MMEA AEMM MMAE MMEA MEAM AMME MEMA AMME AMEM AEMM The other thing that I found out was that in JACK there are 24 different arrangements but in EMMA

  • Word count: 1443
  • Level: GCSE
  • Subject: Maths
Access this essay

Emma's Dilemma

First I wrote out all the possibilities for EMMA using the letters A, B and C instead of E, M and A. These are my results: ABBC ABCB ACBB BABC BACB BBCA BBAC BCAB BCBA CABB CBAB CBBA There are 12 different arrangements. A shorter way of finding this is by using the number of arrangements for a four-letter word with all different letters. In my table of results I found that by using the equation n(n-1) x n(n-2) ... 3x2x1 equals the number of arrangements for any number of letters. Then I looked up an A-Level text book which explained that n(n-1) x n(n-2) ... 3x2x1 is equal to n factorial (n!). Using this I experimented with the different sums to try and work out a direct way to find out the number of different arrangements for a word which has 2 letters the same. I then wrote out the possibilities for a 3-letter word with two letters the same in order to fill in my table of results to get a solution. AAB ABA BAA NUMBER OF LETTERS n! 2 LETTERS THE SAME 1 1 - 2 2 1 3 6 3 4 24 12 5 120 6 720 I noticed if you dived n! by the number of same letters (2) you get the number of possibilities for a word with a number of a word with 2 same letters. My completed tables of results are on the next page: NUMBER OF LETTERS n! 2 LETTERS THE SAME 1 1 - 2 2 1 3 6 3 4

  • Word count: 443
  • Level: GCSE
  • Subject: Maths
Access this essay

Emma's Dilemma

4th January 2002 Emma's Dilemma The Problem: Emma is playing with arrangements of the letters of her name. One arrangement is EMMA A different arrangement is MEAM Another arrangement is AEMM Experiment: For my investigation I have been asked to work out the number of different arrangements of the letters from the name Emma. EMMA AMEM EMAM AMME EAMM MEMA MMEA MMAE MAME MEAM MAEM AEMM I have found out that when the letter "E" is at the front of the name Emma, then there are three different combinations. The same rule applies when the letter "A" is at the front of the name Emma. There is an exception though, when the letter "M" is at the front of the name Emma then there are six different combinations. Overall there are 12 different combinations for the name Emma. For the second part of my investigation I have been asked to work out the number of different arrangements of letters from the name Lucy. LUCY UYCL YCLU LCUY UYLC YULC LCYU CULY YLCU LYCU CUYL YLUC LYUC CLYU LUYC CLUY ULCY CYLU UCLY CYUL UCYL YUCL ULYC YCUL From this second experiment I have found out that when the letter "L" is at the front of the name Lucy then there are six different combinations. The same rule applies to the letters "U", "C" and "Y" in the name Lucy. Overall there are 24 different combinations for the name Lucy From the first two experiments I have

  • Word count: 850
  • Level: GCSE
  • Subject: Maths
Access this essay

Emma's Dilemma

Liu Ted Sam aab 2 Lui Tde Sma aba 3 Uli Det Mas baa 4 Uil Dte Msa 5 Ilu Etd Asm 6 Iul Edt Ams Total rearrangements for words with 3 letters, none of them being the same letter = 6 The total rearrangements for words with 3 letters, 2 of them being the same letter = 3 If a word has three letters, all of them being the same letter, it can not be rearranged. To start this project I am going to write my prediction, followed by the rearrangements of some words. Later I will compare the results and find out if there is a connection between the numbers of rearrangements for different words. I predict that words that have the same number of letters, will have the same number of rearrangements. This is because the words will only have different letters, but the same rearrangements, i.e. I could replace all of the letters in a word with a, b, c etc. Lucy Mary John 2 Luyc Mayr Jonh 3 Lyuc Myar Jnoh 4 Lycu Myra Jnho 5 Lcuy Mrya Jhon 6 Lcyu Mray Jhno 7 Ulcy Amyr Ojnh 8 Ulyc Amry Ojhn 9 Uylc Army Ohnj 0 Uycl Arym Ohjn 1 Ucyl Ayrm Onjh 2 Ucly Aymr Onhj 3 Culy Ramy Honj 4 Cuyl Raym Hojn 5 Cylu Ryam Hjon 6 Cyul Ryma Hjno 7 Cluy Rmya Hnoj 8 Clyu Rmay Hnjo 9 Yclu Yamr Nojh 20 Ycul Yarm Nohj 21 Yucl Ymar Nhjo 22 Yulc Ymra Nhoj 23 Ylcu Yram Njoh 24 Yluc Yrma Njho Total

  • Word count: 1872
  • Level: GCSE
  • Subject: Maths
Access this essay

Emma's dilemma

Emma's dilemma THAMILINI KUGARAJAH CATERHAM HIGH SCHOOL CENTER NO: 13321 CANDIDATE NO: 9191 Introduction: This investigation is about finding the different arrangements of letters in various words. I am going to look at the number of different arrangements for words with all letters different, words with two letters the same and the words with three letters the same and so on. > Part 1 I am going to look at the number of different arrangements of the letters of Lucy's name. LUCY . LUCY 2. LUYC 3. LCYU 4. LCUY 5. LYUC 6. LYLU 7. ULYC 8. ULCY 9. UCLY 0. UCYL 1. UYCL 2. UYLC 3. CYLU 4. CYUL 5. CULY 6. CUYL 7. CLYU 8. CLUY 9. YLUC 20. YLCU 21. YUCL 22. YULC 23. YULU 24. YCUL As it shown above, there are 24 different arrangements in four letter word. C Y U Y C U Y L C Y U C U Y U C A tree diagram can also be used as I have used above. Here we have used "L" as a first letter; however the same process can be used with other 3 letter, so we can multiply the number of letter by the number of possibilities, 6*4=24 Each starting letter has six possibilities. Therefore four letters altogether 6+6+6+6=24 You will get 24 possibilities altogether. First of all we have got 4 possibilities (4 letters) and then 3 possibilities(by leaving first letter "L") and then 2 possibilities 9by leaving first two letters "L"U") after that one

  • Word count: 2463
  • Level: GCSE
  • Subject: Maths
Access this essay

Emma's Dilemma.

Maths Coursework- Emma's Dilemma For this piece of coursework I am going to investigate the number of different ways I can write a word, re-arranging the letters without having any repeats of the sequence. After I have finished my investigations I will try and use my findings to draw together a formula which I could then use to find out how many ways a word can be written for any chosen word. My initial step is to write the name 'EMMA' with as many different arrangements I can find. Part 1 ) EMMA 7) MAME 2) EMAM 8) MEAM 3) EAMM 9) MAEM 4) MMEA 0) AEMM 5) MMAE 1) AMEM 6) MEMA 2) AMME Next I am again going to try a 4 letter word, but this time without repeats (no 2 letters the same) in it. I predict that a 4 letter without repeats will have a lot more letter arrangements than the name EMMA which has 'M' repeated. Part 2- I have chosen the name ANDY. ) ANDY 9) NYAD 7) DYNA 2) ANYD 0) NYDA 8) DYAN 3) ADYN 1) NDYA 9) YADN 4) ADNY 2) NDAY 20) YAND 5) AYDN 3) DNYA 21) YNDA 6) AYND 4) DNAY 22) YNAD 7) NAYD 5) DANY 23) YDAN 8) NADY 6) DAYN 24) YDNA This is double the number of ways EMMA can be written. My first thought to get the number of arrangements is possibly by dividing a value (which I do not know at present) by the number of times a letter is repeated in a word. E.g. SARA would be ?/2, where ? is the unknown value and the 2 is

  • Word count: 1271
  • Level: GCSE
  • Subject: Maths
Access this essay

Emma's Dilemma.

EMMA, EMAM, EAMM, AEMM, AMEM, AMME, MMEA, MMAE, MAEM, MEMA, MEAM, MAME. - There is 12 ways to arrange the word Emma. LUCY, LUYC, LYCU, LYUC, LCUY, LCYU, YUCL, YULC, YCLU, YCUL, YLUC, YLCU, CLYU, CLUY, CULY, CUYL, CYUL, CYLU, UCLY, UCYL, ULCY, ULYC, UYLC, UYCL - There is 24 ways to arrange the word Lucy. A, - 1 letter word, 1 Arrangement TO, OT - 2 letter word, 0 same, 2 arrangements AA - 2 letter word, 2 same, 1 arrangements AMY, AYM, YMA, YAM, MAY, MYA - 3 letter word, 0 same, 6 arrangements AAB, ABA, BAA - 3 letter word, 2 same, 3 arrangements AAA - 3 letter word, 3 same, 1 arrangements KATE, KAET, KTEA, KTAE, KEAT, KETA, TEAK, TEKA, TAKE, TAEK, TKEA, TAKE, EAKT, EATK, ETKA, ETAK, EKTA, EKAT, AEKT, AETK, AKTE, AKET, ATEK, ATKE - 4 letter word, 0 same, 24 arrangements EMMA, EMAM, EAMM, AEMM, AMEM, AMME, MMEA, MMAE, MAEM, MEMA, MEAM, MAME - 4 letter word, 0 same, 12 arrangements AAAB, AABA, ABAA, BAAA - 4 letter word, 3 same, 4 arrangements AAAA - 4 letter word, 4 same, 1 arrangements KATIE, KATEI, KAEIT, KAETI, KAITE, KAIET, KTAIE, KTAEI, KTEIA, KTEAI, KTIAE, KTIAE, KIAET, KIATE, KIETA, KIEAT, KITEA, KITAE, KEITA, KEIAT, KEATI, KEAIT, KETIA, KETAI, AKTIE, AKTEI, AKEIT, AKETI, AKITE, AKIET, ATKIE, ATKEI, ATEIK, ATEKI, ATIKE, ATIKE, AIAKT, AIKTE, AIETK, AIEKT, AITEK, AITKE, AEITK, AEIKT, AEKTI, AEKIT, AETIK, AETKI, TAKIE, TAKEI, TAEIK, TAEKI, TAIKE, TAIEK, TKAIE,

  • Word count: 859
  • Level: GCSE
  • Subject: Maths
Access this essay

Emma's Dilemma

Different combinations of letters for the name Emma: . EMMA 2. MEAM 3. AEMM 4. EAMM 5. MMEA 6. MMAE 7. AMEM 8. EMAM 9. MAEM 0. MEMA 1. MAME 2. AMME Different combinations of letters for the name Lucy: . LUCY 2. ULCY 3. CLYU 4. YCLU 5. LUYC 6. ULYC 7. CLUY 8. YCUL 9. LCUY 0. UCYL 1. CULY 2. YULC 3. LCYU 4. UCLY 5. CUYL 6. YUCL 7. LYCU 8. UYCL 9. CYLU 20. YLCU 21. LYUC 22. UYLC 23. CYUL 24. YLUC The method that I have used to find the number of combinations of letters for these two names could be called manual. I have taken one letter from the name, and added to it the different combinations of the remaining three letters. I did that for every letter in the word, and that is how I reached 24 combinations. I have noticed that both names have 4 letters in them, but the name "Emma" only have 12 combinations. The reason for this is that the word has two letters that are the same (MM). Later on in this coursework I will state, and explain the formulae that can be used to find the number of combinations of letters for words that have two or more of the same letters in them. I have also noticed that there are only 6 possible combinations per letter. So there are 4 letters in the word. If I multiply 6 with 4, that gives me 24 different combinations. At this

  • Word count: 1389
  • Level: GCSE
  • Subject: Maths
Access this essay

Emma's Dilemma.

Emma and Lucy are playing with combinations of the letters of their names. One arrangement of Lucy is YLUC. Another is LYCU. Part 1 - The different combinations of the letters of Lucy's name. Below are all the different combinations of the name Lucy. . LUCY 2. LUYC 3. LCYU 4. LYCU 5. LCUY 6. LYUC 7. UCYL 8. UCLY 9. UYLC 0. UYCL 1. ULYC 2. ULCY 3. CLUY 4. CLYU 5. CULY 6. CUYL 7. CYUL 8. CYLU 9. YLUC 20. YLCU 21. YUCL 22. YULC 23. YCLU 24. YCUL The name Lucy has 24 different combinations. This means that all names with 4 different letters will have a total of 24 different combinations. Looking at other, similar, names with 4 different letters such as Mark, we can see this. Below are all the different combinations for the name Mark. . MARK 2. MAKR 3. MRKA 4. MRAK 5. MKAR 6. MKRA 7. ARKM 8. ARMK 9. AKRM 0. AKMR 1. AMKR 2. AMRK 3. RKMA 4. RKAM 5. RMKA 6. RMAK 7. RAKM 8. RAMK 9. KRAM 20. KRMA 21. KMAR 22. KMRA 23. KARM 24. KAMR As you can see the name MARK also has 24 different combinations. Calculations The number of combinations for the name Lucy can be worked out in the following ways. . no. of letters + 2 x no. of letters [4+2 x 4 = 24] 2. no. of letters factorial [4! = 1x2x3x4 = 24] To see if the above methods work, we can test them on the three (different) letter name Ian. Below are

  • Word count: 1262
  • Level: GCSE
  • Subject: Maths
Access this essay