First let me apologise for the improper use of 'groups'. I'm not a mathematician but I know that 'groups' means something specific.(adsbygoogle = window.adsbygoogle || []).push({});

Anyway, here is my problem. The exact circumstances of my problem are esoteric and bothersome to explain, and I don't want to distract you with details that do not matter (but I will if you ask ;-) so I am simplifying somewhat.

I look after a database that contains recipes for about 1000 products. Each product contains one or more ingredients. Some ingredients are used in many products, other ingredients are used in only a handful of products. Every product has a label that lists the ingredients. There are approximately 600 different ingredients.

I need to update the information in my database about the ingredients. For the sake of argument, lets say I need to just spell them in capital letters, but in reality I am doing something more involved. Because I have changed the spelling of my ingredients, I need to update the labels of the products that contain those ingredients.

Changing the spelling of all 600 ingredients will take a very long time, so I need to split the 600 ingredients up into smaller groups.

Updating the label of each product is expensive, so I only want to do it once per product. This means that when I divide the list of ingredients into groups, all of the products that contain these ingredients must contain only these ingredients.

The question is "what process should I use to decide how to divide up my list of ingredients"?

Thanks very much for your thoughts and advice

Mx

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# Real-world logic problem with statistics and groups

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