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Emma's Dilemma Emma is playing with arrangements of the letter of her name. One arrangement is E M M A Another arrangement can be: E M AM In this investigation I am going to investigate the different number of letters in a word, and see if there are any patterns. The first two names I will investigate are EMMA and LUCY. EMMA EMAM EAMM AEMM AMEM AMME MMEA MMAE MEAM MAEM MEMA MAME There are 12 different arrangements for the name EMMA. LUCY LUYC LYUC LYCU LCYU LCUY ULCY ULYC UYCL UYLC UCLY UCYL CULY CUYL CYLU CYUL CLUY CLYU YCUL YCLU YLUC YLCU YUCL YULC There are 24 different arrangements for the name LUCY. Despite both names having the same amount of letters, there are a different number of arrangements. This is because in EMMA there are 3 different letters, and in LUCY there are 4 different letters. First I will investigate words in which all the letters are different. A 1 letter word, such as A only has 1 arrangement: A A 2 letter name such as JO has 2 arrangements: JO OJ A 3 letter name such as TOM has 6 arrangements: TOM TMO MOT MTO OTM OMT A 4 letter name such as...

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