Which supervised learning algorithm to classify customers buying items I am very new to machine learning, and it's hard for me to know in what direction I should go. Thanks in advance for your help.

I have a set of data showing what customers bought:


A customer may have bought 1 or more items
Each item is discribed by :


A quality level which is an integer between 1 and 7
Its content from a first point of view (the item has x1% of content 1, x2% of content 2, ...)
Its content from a second point of view (the item has xA% of content A, xB% of content B, ...)

A customer says that he belongs to the group G1, G2 or G3


I would like to be able to guess the group a new customer belongs to, given the items he bought.

What algorithm should I ideally use ?
What algorithm would you recommend if I can only use numpy, without scipy or scikit (it's on a server which only has numpy) ?

Thank you very much

Edit : I'm adding the appropriate words to the title and to the tags
As per the problem statement statement it does look like 3 class classification problem. 
But I don't think you can use any ML algorithms using Python without sklearn package in it. Try getting it installed and you can implement the problem using Logistic regression, Decision Tree, there are still more classification algorithms.
However if you are planning to extract a pattern from the dataset and making into cluster, you can use K-means clustering which is a un-supervised algorithm.