The objective of this coursework is to find the formula that gives the maximum product of any given number when split into parts. For the first part of the coursework I am going to investigate the splitting of a number into two parts, then three parts and four Parts. For each number of parts, This will result with a formula that gives the maximum product. Pairs Starting number 12, PAIRS WHICH TOTAL 12 & PRODUCT OF THE PAIR 12,0 = 0 11,1 = 11 10,2 = 20 9,3 = 27 8,4 = 32 7,5 = 35 6,6 = 36 5,7 = 35 4,8 = 32 3,9 = 27 10 = 20 1,11 = 11 0,12 = 0 …showed first 75 words of 806 total…

…showed last 75 words of 806 total…as it is the highest. Starting number 14 QUADRUPLES WHICH TOTAL 14 & PRODUCT 14,0,0,0 =0 11,1,1,1 =11 10,1,1,2 =20 9,1,2,2 =36 8,2,2,2 =64 7,2,4,1 =56 6,6,1,1 =36 5,4,4,1 =80 4,4,4,2 =128 3,4,6,1 =72 2,3,3,6 =108 TEST FOR THE MAXI PRODUCT 3.75 x 3.25 x 3 x 4= 146.25 I am going to try a different combination 3.5 x 3.5 x 3.5 x 3.5=150.06 That is the maxi product. STARTING NUMBERS QUADRUPLES THAT GIVE MAXI PRODUCT VALUE 12, 3x 3 x 3 x3 =81 16, 4 x 4 x 4 x 4 =256 14, 3.5 x 3.5 x 3.5 x 3.5 =150.06 M= n/4 x n/4 x n/4 x n/4 = (¨ù)4 M again represents the Maxi Product and n represents the Starting number. The formula is (¨ù)3 .