GCSE Mathematics - Bad tomatoes

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Dale Jacques 22nd June 2001

GCSE Mathematics

Bad tomatoes

Identical 'good' Tomatoes are placed in a tray.

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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.

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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.

st hour

2

, 6, 9

2nd hour

4

2, 7, 10, 13

3rd hour

4

3, 8, 11, 14

4th hour

3

4, 12, 15

5th hour

6

What would happen if tomato no.1 was the bad tomato?

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Hours

No of bad tomatoes

Bad tomato no.

st hour

2

2, 5

2nd hour

3

3, 6, 9

3rd hour

4

4, 7, 10, 13

4th hour

3

8, 11, 14

5th hour

2

2, 15

6th hour

6

What would happen if tomato no.6 was the first bad tomato?
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Hours

No of bad tomatoes

Bad tomato no.

st hour

4

2, 5, 7, 10

2nd hour

6

, 3, 8, 11, 9, 14

3rd hour

4

4, 12, 13, 15

4th hour

6

I have found out that if tomato no.5 goes bad first it would take the same amount ...

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