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By Payam Gammage Introduction The aim of these investigations is to explore and find a relationship between the number of letters in a word and the number of arrangements of the letters there are. 1. LUCY For these investigations, I have decided to use numbers instead of letters because it will be easier to work out all of the arrangements if I can do them in numerical order. I have numbered the letters: L = 1 U = 2 C = 3 Y = 4 I have started by writing out all the combinations beginning with 1 (L) and then 2 (U), 3(C) and so on 1234 = LUCY 3124 = CLUY 1243 = LUYC 3142 = CLYU 1324 = LCUY 3214 = CULY 1342 = LCYU 3241 = CUYL 1423 = LYUC 3412 = CYLU 1432 = LYCU 3421 = CYUL 2134 = ULCY 4123 = YLUC 2143 = ULYC 4132 = YLCU 2314 = UCLY 4213 = YULC 2341 = UCYL 4231 = YUCL 2413 = UYLC 4312 = YCUL 2431 = UYCL 4321 = YCLU As you can see, there are 24 possible combinations, six beginning with each number. I know that I have found all the possible arrangements because I have written them out in numerical order starting with the smallest (1234 or LUCY) then largest (4321 or YCUL). I have also made an observation that the letters in the largest number are exactly the reverse...

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