There is a place known as the Pizzeria at the End of the World. They serve pizzas but who doesn’t? They have also installed some computer software to collect orders and to analyze the incoming data for all kinds of patterns and regularities which may occur. Just to be ready for every customer’s whim and for always changing trends and demands. It becomes a science, selling pizzas these days, but what doesn’t?
So, one night, after closing the shop, papa and mamma are driving home. “You know”, started the wife, “computer says, today, there were no two same orders, looking by kinds of pizza served to a table. Not two, despite the fact it was a lot of customers and a lot of pizzas sold!”
“Really?”, says the husband. “Two orders are the same by pizza kinds, if and only if, for every kind of pizza on one order, there is this very same kind of pizza on the other order as well?”
“Yes.”, says the wife, her name was Martha, “One Margarita with two Hawaiian pizzas or two Margaritas with three Hawaiian pizzas are not equal orders, but they are equal by pizza kinds!”
“Very well”, says the husband, his name was Marco, “At least one of those two possible orders was not ordered today, right? And the salads and drinks are all ignored here, am I right?”
“You are always right!”, says Martha. “Moreover, the computer says, that for every pair of orders today, there was one order equal to those two orders combined! Equal by pizza kinds, that is!”
“What an amazing coincidence!”, says Marco. “This computer is too smart for his own good!”
“I wonder”, says Martha, “if there is a kind of pizza ordered today, present on the majority of all orders?”
“Ask the computer”, says Marco, “if there is an order with only one kind of pizza on it.”
“Computer says there is not. This might be good for our business.”, replied Martha.
Then the Wifi connection to the computer back at the Pizzeria at the End of the World, somehow disconnected. So Martha and Marco were on their own for a while.
He says: “You know dear, probably there was a pizza so popular today, that the majority of orders did contain it. I don’t know which one. Today’s state of the art mathematics isn’t powerful enough to ascertain that this is actually the case!”
“Yeah, I realize this now!”, says Martha. “We’ll wait until tomorrow to see. If there is and which one it is.”
Question. At least how many varieties or kinds of pizzas are served at the place, known as the Pizzeria at the End of the World? Assuming the computer, Martha, and Marco are all correct at everything they spoke.
It’s not a trick question, or a joke, or something of that kind.
Solution is here: