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The Partitions of 12.
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| Submitted: Fri Nov 07 2003
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Year 9 Maths Coursework By Rahul Dey Form: 9P Contents 3. Coursework Version History 4. Question 1 5-9. Question 2 10. Question 3 Coursework Project History Version 1.0 - Added all of the needed information into the coursework. Version 1.1 - Neatened up layout of partitions, and elaborated briefly on some ideas Version 1.2 - Put all of the partitions into tables to save space, and to neaten it up. Question 1 The Partitions of 12: Using the following systematic process, the number 12 can be partitioned into the following pairs: First Integer Second Integer Product 12 0 0 11.5 0.5 5.75 11 1 11 10.5 1.5 15.75 10 2 20 9.5 2.5 23.75 9 3 27 8.5 3.5 29.75 8 4 32 7.5 4.5 33.75 7 5 35 6.5 5.5 35.75 6 6 36 5.5 6.5 35.75 5 7 35 4.5 7.5 33.75 4 8 32 3.5 8.5 29.75 3 9 27 2.5 9.5 23.75 2 10 20 1.5 10.5 15.75 1 11 11 0.5 11.5 5.75 0 12 0 (NOTE: I HAVE ALSO PUT THE PRODUCT COLUMN HERE TO SHOW THE PRODUCTS OF THE TWO PARTITIONING INTEGERS WHEN MULTIPLIED) Due to the fact that there are infinite partitions of the number 12 (and indeed any other number), I have only broken them down into halves, to show that it works with fractional numbers. Answer: The answer to question 1 is 6x6. This is because 6x6 gives the highest product when multiplies together. Notes: I notice that there...
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