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 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

I will assume my maxi product is in the range between 7,5 and 5,7 because this where the product is at it¯s highest. So, 6.9 ¿ 5.1=35.19, 5.9 ¿ 6.1=35.99 Neither of these are higher than 36. So for my starting number 12, I have used the pairs 6 and 6 and my maxi product is 36.

PAIRS WHICH TOTAL 10 & PRODUCT OF THE PAIRS

10,0 = 0 9,1 = 9 8,2 = 16 7,3 = 21 6,4 = 24 5,5 = 25 4,6 = 24 3,7 = 21 2,8 = 16 1,9 = 9 0,10 = 0

The maxi product lies between 6,4 and 4,6 because it these two numbers have the highest product. 5 x 5=25, 6 ¿ 4=24, 4.5 ¿ 5.5=24,75. Neither of the pr

16,0=0 15,1 =15 14,2 =28 13,3 =39 12,4 =48 11,5 =55 10,6 =60 9,7 =63 8,8 =64 7,9 =63 6,10 =60 5,11 =55 4,12 =48 3,13 =39 2,14 =28 1,15 =15 0,16 =0

The maxi product lies between 8,6 and 6,8 as this is where the product is highest. 7 ¿7=49 7.9 ¿ 6.1=48.19 6.9 ¿ 7.1=48.99. For my starting number 14, I have used 7,7 and my maxi product is 49.

Some common words found in the essay are:
MAXI PRODUCT, PRODUCT PAIRS, TRIPLE TOTAL, QUADRUPLES TOTAL, MAXIPRODUCT VALUE, PRODUCT VALUE, PRODUCT PAIR, maxi product, Maxi Product, MAXIMUM PRODUCT, PAIRS TOTAL, test maxi product, test maxi, 4 4, maximum product, 35 35, product pairs, pairs total, product starting, product maxi product, product maxi, product lies, maxi product lies, maxi product maxi, =0 test maxi,
Approximate Word count = 1546
Approximate Pages = 6 (250 words per page double spaced)