Bad Tomatoes

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Bad Tomatoes

Bad Tomatoes

Identical good tomatoes are placed in a box (see example).

Each tomato is a sphere. Each tomato just touches all the other tomatoes next to it as shown in the diagram. Tomato five goes bad. This is counted as the first hour. One hour later, all the tomatoes it touches go bad (now tomatoes 5,1,6 and 9 are bad). This continues every hour untill all the tomatoes in the box are bad.

I aim to investigate how tomatoes go bad in the above tray, and in trays of different sizes.

How do tomatoes go bad in trays?

In this investigation, I aim to find a formula for calculating the total time required for all tomatoes to go bad in a rectangular tray of any rectangular size, and with any bad tomato starting position. To achieve this, I will first need to explain with the use of diagrams, how I arrived at a formula for the total time required for the tray to go bad. This will be done in three stages, followed by a worked example, which will answer both part 1 of the investigation, and part 2. Part