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  • Level: GCSE
  • Subject: Maths
  • Word count: 1724

GCSE Mathematics - Bad tomatoes

Extracts from this document...

Introduction

Dale Jacques 22nd June 2001 GCSE Mathematics Bad tomatoes Identical 'good' Tomatoes are placed in a tray. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Tomato no. 5 is the bad tomato Each tomato is a sphere. Each tomato just touches all the tomatoes next to it as shown on the diagram. Tomato 5 goes bad first. One hour later, all the tomatoes it touches go bad (Now tomatoes 5, 1, 6 and 9 are bad). Another hour later the bad tomatoes make all the good tomatoes they touch go bad. This continues until all the tomatoes in the box are bad. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E.g. no. 5 is the bad tomato 1-hour later tomatoes no.1, 6 and 9 are bad. Another hour later tomatoes 2, 7, 10 and 13 are bad. Another hour later tomatoes 3, 8, 11 and 14 are bad. Another hour later tomatoes 4, 12 and 15 are bad. Another hour later tomato 16 is bad. Hours No of bad tomatoes Bad tomato no. ...read more.

Middle

5th hour 2 24, 20 6th hour 1 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Hours No of bad tomatoes Bad tomato no. 1st hour 4 3, 7, 9, 13 2nd hour 7 2, 4, 6, 10, 12, 14, 18 3rd hour 7 1, 5, 11, 15, 17, 19, 23 4th hour 4 16, 20, 22, 24 5th hour 2 21, 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Bad tomato no. 13 Hours No of bad tomatoes Bad tomato no. 1st hour 8,12,14,18 4 2nd hour 3,7,9,11,17,23,19,15 8 3rd hour 2,6,16,22,24,20,4,10 8 4th hour 1,5,21,25 4 In this example I will change the size of the tray, this might affect which no. Tomato will be the last one to go bad. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Hours No of bad tomatoes Bad tomato no. ...read more.

Conclusion

1st hour 4 9,14,16,21 2nd hour 7 3,8,10,13,17,20,22,27 3rd hour 8 2,4,7,11,18,19,23,26,28,33 4th hour 7 1,5,12,24,25,29,32,34, 5th hour 4 6,30,31,35 6th hour 1 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Now I will look for a pattern in my results. For a 4x4 tray L=4 I will put the results into a table and connect the no. Of hours it takes for the whole tray to go bad. I will try and do different formulae for each diagonal. For diagonal 1 (The corners) L= No. 4 6 5 8 N=2L 6 10 Middle L No. 4 5 5 7 N=2L-3 6 9 3rd diagonal L No. 4 4 5 6 N=2L-4 6 8 2L-Diagonal+1 N=2L-(D+1) Now I need to test my formula. 1 2 3 4 5 6 7 8 9 For a 3x3 corners L=3 D=1 So n should be N=2L - (D+L) =2 x 3 - 1+ 1 =6 - 2 =4 ...read more.

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