Emma’S Dilemma

GCSE Maths

Daniel Kerrigan 11.2

EMMA’S DILEMMA

I will now try some simple cases of rearranging letters to count the number of different combinations.

TWO LETTER WORDS:

AB BA

CC

THREE LETTER WORDS:

ABC ACB BAC BCA CBA CAB

ABB BAB BBA

FOUR LETTER WORDS:

CLUY CLYU CULY CYLU CYUL CUYL LUCY LYCU LCYU LCUY LUYC UYCL UYLC ULCY ULYC UCYL UCLY YCUL YCLU YLCU YLUC YUCL YULC

AEMM AMME AMEM EMMA EAMM EMAM MEMA MEAM MMEA MMAE MAME MAEM

RESULTS TABLE:

In my table I have spotted a pattern. The pattern is when a name has two letters the same it only has half the combinations of a name with all letters different.

PREDICTION:

I predict that if a word has 2 of the same letters then it has half the number of combinations than a word with the same amount of letters, of which all are different.

I will now test my prediction on 2, five-letter words. I will use a five-letter word with two letters that are the same such as David. I will also use a five-letter word with all the letters different such as Craig.

DAVID DAVDI DADIV DADVI DAIDV DAIVD DIAVD DIADV DIDAV DIDVA DIVDA DIVAD DVIAD DVIDA DVDIA DVDAI DVADI DVAID DDVAI DDVIA DDIVA DDIAV DDAIV DDAVI ADDVI ADDIV ADIVD ADIDV ADVDI ADVID AIDVD AIDDV AVDDI AVDID AVIDD AIVDD IAVDD IADVD IADDV IDADV IDAVD IDVAD IDVDA IDDVA IDDAV IVADD IVDAD IVDDA VIADD VIDAD VIDDA VDIAD VDIDA VDDIA VDDAI VDADI VDAID VADDI VADID VAIDD

ACIGR ACIRG ACRIG ACRGI ACGIR ACGRI AICGR AICRG AIGCR AIGRC AIRGC AIRCG AGIRC AGICR AGCIR AGCRI AGRCI AGRIC ARCIG ARCGI ARICG ARIGC ARGIC ARGCI CAIGR CAIRG CAGIR CAGRI CARGI CARIG CIARG CIAGR CIGAR CIGRA CIRGA CIRAG CGAIR CGARI ...