Emma's dilemma The different ways of arranging letters for Emma's name
Emma's dilemma There are different ways of arranging letters for Emma's name the combinations for Emma's name are EMMA MMAE MMAE EAMM AEMM MEMA MAME MEAM MAEM AMME AMEM EMAM There are 12 combinations for a 4 letter word with 2 repeats Emma has a friend called Lucy. Lucy wants to find how many different combinations her name makes ABCD ACDB ADBC ACDB ACBD ADCB DCAB DCBA DBAC DBCA DACB DABC CBAC CBDA CDBA CDAB CABD CADB BADC BACD BCDA BCAD BDCA BDAC. There are 24 different combinations for a 4 letter word with no repeats Letter A 2 Letters AB BA 3 Letters ABC ACB BAC BCA CAB CBA 4 Letters ABCD ACDB ADBC ACDB ACBD ADCB DCAB DCBA DBAC DBCA DACB DABC CBAC CBDA CDBA CDAB CABD CADB BADC BACD BCDA BCAD BDCA BDAC. No. letters combinations = 1 x 1 2 2 = 1 x 2 3 6 = 2 x 3 4 24 = 6 x 4 5 ? = 5 x 24 The rule is times the number of letters by the number of combinations of the previous number using this rule I can predict the 5 letters will have 120 different combinations because the previous number of combinations was 24 and the number of letters is 5 so 5 x 24 =120 There is an easier and quicker way to find how many combinations there are for a certain number this is called N factorial written as N! (N stands for the number of letters you have). N factorial times all the numbers from the number or letters you have all the way to 1 for example if you
Dave's Dilemma
Maths Coursework . Investigate the number of arrangements of Dave's name......... DAVE DAEV DEAV DEVA DVAE DVEA ADEV ADVE AEDV AEVD AVED AVDE VDAE VDEA VEDA VEAD VAED VADE EVDA EVAD EDVA EDAV EAVD EADV There are 24 different arrangements for Dave's name. * For a two letter word (AT) , there are two arrangements. AT TA * For a three letter(CAT) word, there are six arrangements. CAT CTA ACT ATC TAC TCA * For a four letter word (LEAD), there are twenty-four arrangements. LEAD LEDA LAED LADE LDEA LDAE DEAL DELA DLEA DLAE DALE DAEL ADEL ADLE ALED ALDE AEDL AELD EALD EADL EDAL EDLA ELDA ELAD * For a five letter word (SOUTH), there are one hundred and twenty arrangements. SOUTH SOTUH SOHUT SOUHT SOHTU SOTHU SUOTH SUOHT SUHOT SUHTO SUTOH SUTHO STUHO STUOH STHUO STHOU STOHU STOUH SHTOU SHTUO SHUOT SHUTO SHOYU SHOUT OSUTH OSUHT OSHUT OSHTU OSTHU OSTUH OTSUH OTSHU OTHSU OTHUS OTUSH OTUHS OUTHS OUTSH OUSTH OUSHT OUHST OUHTS OHUTS OHUST OHSUT OHSTU OHTSU OHTUS UOSTH UOSHT UOHST UOHTS UOTSH UOTHS UTOHS UTOSH UTSOH UTSHO UTHOS UTHSO USTHO USTOH USOTH USOHT USHOT USHTO UHTSO UHTOS UHOTS UHOST UHSTO UHSOT THUOS THUSO THSUO THOSU THOUS TSHOU TSHUO TSUHO TSUOH TSOUH TSOHU TOSHU TOSUA TOUSH TOUHS TOHSU TOHUS TUHSO TUHOS TUSOH TUSHO TUOHS
I am investigating the number of different arrangements of letters in a word.
I am investigating the number of different arrangements of letters in a word. The name Emma has 12 different combinations. 24 combinations * LUYC * LCYU * LCUY * LYCU * LYUC * UCLY * UCYL * ULCY * ULYC * UYLC * UYCL * CUYL * CULY * CLUY * CLYU * CYUL * CYLU * YCLU * YCUL * YULC * YUCL * YLCU * YLUC The name Lucy has 4 letters with 24 combinations. 2 letters * Jo 2 combinations * Oj The name Jo has 2 letters with 2 combinations 3 letters * Sam 6 combinations * Sma * Ams * Asm * Mas * Msa The Name Sam has 3 letters with 6 combinations 5 letters * D(iego) =24 + * I (dego) =24 + * E (digo) =24 + * G (dieo) =24 + * O (dieg) =24 + =120 Total no. Of letters No repeated letters 2 2 3 6 4 24 5 20 In a 4-letter name such as Lucy, the way to work out the number of combinations is to do 4 x 3 x 2 x 1 or 4 factorial (4!). . Factorial is a number multiplied by the previous consecutive numbers. Factorial notation is symbolised using an exclamation mark! So I came to conclude that the formula to work out any the combinations is the numbers of letters factorial equals arrangements (l! =a). With this formula in mind I can predict the number of arrangements for an 8-letter name. 8! (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) =40320 When there are repeated letters like in EMMA there are 12 combinations. EMMA AMME AMEM EMAM AEMM EAMM
Investigate the number of different arrangements of the letters in a name.
Page 1 Emma's Dilemma Emma is playing around with arrangements of the letters of her name. One arrangement is EMMA, a different arrangement is MEAM. Another arrangement is AEMM. . Investigate the number of different arrangements of the letters of Emma's name. . EMMA 2. AEMM 3. MAEM 4. MMAE 5. MMEA 6. AMME 12 WAYS 7. EAMM 8. MEAM 9. MEMA 0. AMEM 1. MAME 2. EMAM Emma has a friend called Lucy. 2. Investigate the number of different arrangements of the letters of Lucy's name. . LUCY 2.YLUC 3. CYLU 4. UCYL 5. UCLY 6. YUCL 7. LYUC 8. CLYU 9. CLUY 0. YCLU 1. UYCL 2. LUYC 3. ULYC 4. CULY 5. YCUL Page 2 6. LYCU 24 WAYS 7. YLCU 8. UYLC 9. CUYL 20. LCUY 21. LCYU 22. ULCY 23. YULC 24. CYUL Choose some different names. 3. Investigate the number of different arrangements of the letters of the names you have chosen. These names all have all letters different: 1.Jo 2.Max 3.Mark 4.James . JO 2 WAYS 2. OJ . MAX 2. XMA 3. AXM 6 WAYS 4. AMX 5. XAM 6. MXA . MARK 2. KMAR 3. RKMA 4. ARKM 5. ARMK 6. KARM 7. MKAR Page 3 8. RMKA 9. RMAK 0. KRMA 1. AKRM 2. MAKR 3. AMKR 4. RAMK 24 WAYS 5. KRAM 6. MKRA 7. KMRA 8. AKMR 9. RAKM 20. MRAK 21. MRKA 22. AMRK 23. KAMR 24. RKAM . JAMES 2. SJAME 3. ESJAM 4. MESJA 5. AMESJ 6. AMEJS 7. SAMEJ 8. JSAME 9. EJSAM 0. MEJSA 1. AMEJS 2. AMJES 3.
Ivy Rowe's ideas of the past in Fair and Tender Ladies.
Logan Buccolo English 101 Mr. Butler December 9, 2001 Ivy Rowe's Ideas of the Past in Fair and Tender Ladies In Lee Smith's Fair and Tender Ladies, Ivy Rowe has a constant attachment to her past. This attachment is one of the main themes in the novel. It is one of her main reasons for letter writing and why she does some of the things that she does, because she does not want to lose her grip on her past. Ivy Rowe, in Lee Smith's Fair and Tender Ladies, uses letter writing to keep a hold of her grip on the past and where she came from. In Letters from Sugar Fork, Ivy writes for a number of reasons. She wants to see how and what other people are doing, wanting to improve her writing skills, asking for help from her grandfather at one point, in addition to just having some way to release all her thoughts and emotions. These letters, being a window into her mind, show us the progression of her as she grows. There is one letter in particular, which shows how important this correspondence is to her. "I hate you, you do not write back nor be my Pen Friend I think you are the Ice Queen instead. I do not have a Pen Friend or any friend in the world, I have only Silvaney who laghs and laghs and Beulah who is mad now all the time and Ethel who calls a spade a spade...I will not send this letter as I remain your hateful, Ivy Rowe."(Smith, 17) This letter shows just how important
I will find all the different combinations of Emma's name by rearranging the letters. Following this, I will do the same with Lucy's name and compare
By Emily Kho - 10GGW Maths Investigation: Emma's Dilemma Introduction: During my investigation, I will explore the number of arrangements of different names. My aim is to find a general formula which will enable me to work out the number of arrangements for any name. I will begin this investigation with the name EMMA. Method: I will find all the different combinations of Emma's name by rearranging the letters. Following this, I will do the same with Lucy's name and compare my results. All the letters in Lucy's name are different so, I will investigate the number of permutations for names with different letters. From my results, I will devise a formula for names with different letters. Emma's name has two letters which are the same so I will investigate the numbers of alternative combinations for names where two letters are the same. I will do the same for names where three letters are the same. I will compare these with my original results and work out a formula for names with different letters. My final investigation will be with names with sets of same letters e.g. ANNA. At the end, I will have a formula for all names. I am going to begin by investigating the number of arrangements in Emma's name. Emma EMMA EMAM EAMM AMME AMEM AEMM MEAM MAEM MMEA MMAE MEMA MAME I have found 12 different combinations for Emma's name. I will now investigate the number of
Johannes Gensfleisch zur Laden zum Gutenberg, or commonly know as Johann Gutenberg, was the inventor of the printing press. He was born in Mainz around 1397 and lived until around 1468. He is most known for his inventing of a movable type
Johannes Gutenberg, Inventor of the Printing Press Johannes Gensfleisch zur Laden zum Gutenberg, or commonly know as Johann Gutenberg, was the inventor of the printing press. He was born in Mainz around 1397 and lived until around 1468. He is most known for his inventing of a movable type, that used metals and alloys, and a press that used an oil-based ink. This printing method was used up until the 20th century. Much evidence suggests that Gutenberg was born in Mainz, although little is known about his youth. He was born third child of Frelie zum Gensfleisch, and his second wife, Else Wirick zum Gutenberg. (Johann Gutenberg 1) His father was a merchant, and his surname "zum Gutenberg" was established because of the neighborhood, which they lived. (Johann Gutenberg II) He learned the trade of goldsmith while living in Mainz. However in the 1428's, he and his family had to leave due to a revolt of the craftsmen against the nobles. So, around 1430, he went to live in Strassburg, where he remained until around 1444. (Johann Gutenberg 1) In Strasbourg, he joined a Goldsmith's guild, where he taught various crafts, such as gem polishing, the manufacturing of looking glasses, and the art of printing. (Johannes Gutenberg I) He worked with friends and taught them his secret profession of printing, eventually establishing his own, new better way of printing, for which he is most
Find out how many different arrangements of letters there are in a name or word.
EMMA'S DILEMMA In this piece of coursework, I am going to find out how many different arrangements of letters there are in a name or word (according to the number of letters). I will then try to find a pattern in the arrangements that will help me to form an equation. I will also try to find out how many different arrangements there are in a word with two or more sets of different letters that occur more than once. E.g. Xxyyaa .I know this sounds very confusing but you'll soon understand what I'm talking about. By the end of this piece of course work, I should be able to find out how many arrangements there are in XXXYYVVVV by using an equation. ) My first name will be EMMA: )EMMA 2)AMME 3)MMEA 4)MEAM 5)EAMM 6)EMAM 7)AMEM 8)AEMM 9)MAEM 0)MMAE 1)MEMA 2)MAME I have concluded that there are 12 different arrangements in this name. I used various methods to find out the different arrangements: I would put the letter at the beginning on the end each time. E.g. EMMA, MMAE, MAEM etc. I would reverse the words, EMMA, AMME, MEAM, MAEM and so on. 2) The next name I will use is LUCY: )LUCY 2)LCYU 3)LUYC 4)LYUC 5)LCUY 6)LYCU 7)UCYL 8)UCLY 9)UYLC 0)UYCL 1)ULYC 2)ULCY 3)CYLU 3)CYUL 5)CLUY 6)CLYU 7)CUYL 8)CULY 9)YULC 20)YUCL 21)YCUL 22)YCLU 23)YLUC 24)YLUC This shows that there are 24 different arrangements in LUCY. This is double the amount of EMMA.
Emmas dilemma.
Arrangements for EMMA: EMMA EMAM EAMM MMAE MMEA MEAM MEMA MAME MAEM AMME AMEM AEMM Arrangements for MIKE MIKE MIEK MKEI MKIE MEIK MEKI IKEM IKME IEMK IEKM IMEK IMKE KEMI KEIM KIME KIEM KMEI KMIE EMIK EMKI EKMI EKIM EIMK EIKM If I choose a word where all of the letters are different there will be more combinations. There were 24 different possibilities in the arrangement of 4 letters that are all different. That is twice as many as EMMA, which has four letters and 2 the same. I have noticed that with MIKE there were 6 possibilities beginning with each different letter. For instance there are 6 arrangements with MIKE beginning with M, and 6 beginning with I and so on. 6 X 4 (the amount of letters) gives 24, the number 6 may have come from 1 x 2 x 3, the number of letters, and multiplied by four because that is how many numbers there are all together. The difference between how many combinations of the names EMMA and MIKE is the double M in EMMA. There are 24 possible combinations for MIKE and 12 for EMMA. I will now investigate further words with all letters different. I will now test a word with 3 letters: DOG OGD GDO DGO ODG GOD There are 6 possible combinations, 2 for each letter. Now I will investigate a 2 letter word. IT TI There are two possible arrangements, one for each letter. I will now draw a table of results: Number of
We are investigating the number of different arrangements of letters.
EMMA's Dilemma We are investigating the number of different arrangements of letters. Firstly we arrange EMMA's Name. )EAMM 7)MAEM 2)EMAM 8)MAME 3)MEMA 9)AMME 4)MEAM 10)AEMM 5)MMEA 11)AMEM 6)MMAE 12)EMMA Secondlywe arrange lucy's name. )Lucy 12)Cyul 22)Yulc 2)Luyc 13)Culy 23)Ycul 4)Lycu 14)Culy 24)Yluc 5)Lcuy 15)Cylu 25)Ucyl 6)Lcyu 16)Clyu 7)Ulcy 17)Cuyl 8)Ucly 18)Yluc 9)Uycl 19)Yucl 0)Ulyc 20)Yclu 1)Uylc 21)Ylcu From these 2 investigation I worked out a method: Step1: 1234---Do the last two number first then you get 1243. 243---Do the last three numbers and try the possibility. 1423. 1432. 1342. 1324, because the number 2 has been the first number of last three numbers, so we don't do it again. Step2: we have list all arrangements of 1 go front, so we do 2 go front. 2134 and we do same thing to it, it will like this: 2134---2143, 2143---2431,2413,2314,2341 Step3: We have finished 2 go first, then let's do 3 go ahead. 3124---3142, 3142---3241,3214,3412,3421 Step4: We have finished 3 go ahead, then try 4 4123---4132, 4132---4231,4213,4312,4321 We have list all arrangement of 1234, use this method we can arrange the number which has 5 figures or more. We are trying to work out a formula which can calculate the number of arrangement when we look at a number. Let's list all the arrangment for 1234: 234 4123 243 4132 324 --- 6 arrangment 4231 ----