Just an ordinary day in Lake Wobegon

A company has ten customers and three products. Each customer has bought
either none or exactly one of each product.

The following table shows each of the ten customers and what products
they have bought.

* = customer has purchased product
. = customer has not purchased product

customer   product
#          A   B   C
 1         .   .   Y      1 ->     C
 2         .   Y   .      2 ->   B
 3         Y   .   Y      3 -> A   C
 4         Y   Y   .      4 -> A B
 5         Y   .   Y      5 -> A   C
 6         Y   .   .      6 -> A
 7         Y   Y   .      7 -> A B
 8         .   .   Y      8 ->     C
 9         .   Y   Y      9 ->   B C
10         .   Y   Y     10 ->   B C

There are ten customers and 16 total products bought. That means the average customer
has purchased 1.6 products.

Customers 3 through 7 inclusive have each bought product A. There are five such
customers and in total they have bought nine products. That means the average customer
who has bought product A has bought 9/5 products or 1.8 products.

Customers 2, 4, 7, 9, and 10 have bought product B. There are five such customers
and in total they have bought nine products. That means that the average customer
who has bought product B has bought 1.8 products.

Customers 1, 3, 5, 8, 9, and 10 have bought product C. There are six such customers
and in total they have bought ten products. That means that the average customer
who has bought product C has bought 1.66 products.

In other words, in every group of customers, the average customer in that group
has bought more than the average customers. Surely such a company can only exist
in Lake Wobegon where every product's customers are above average.