Tacorama

Overview

Tacorama is a card game for one or more players to find matching families of recipes at a Tex-Mex restaurant. Players are employees angling to impress their boss and get a promotion to night manager. There are several variants of game play, but they all have the basic Tacorama matching rule in common: three recipes go together if the ingredients for two of them can combine to make the third. As these are recipes, it is the ratios of ingredients that matters, not the absolute amounts.

Story

In Tacorama, you and your fellow players are employees of the local Tacorama restaurant, a budget-conscious choice for Tex-Mex food of questionable authenticity and quality. Headquarters has shipped your location a brand new Taco-Maker 5000, an automated taco maker that threatens to put you out of a job! However, your boss has made you and your coworkers an offer: whoever figures out how to prep the most recipes with the Taco-Maker 5000 will receive a promotion to night manager, while everyone else will have to look elsewhere for employment.

The Taco-Maker 5000 is a sophisticated machine that takes between one and four prepackaged kits of two different recipes and prepares a variety of tasty options with different combinations of ingredients. Your task is to take two such recipes and figure out all of the other meals it can prepare. Like all Tacorama meals, Taco-Maker 5000 recipes are made from various ratios of just three ingredients: tortillas, cheese, and ground beef. Each recipe may contain 0 or 1 tortilla, and 0 to 4 helpings of cheese and beef. Recipes must match exactly, without excess ingredients; however, if any ingredient has in excess of five units, the extra ingredients are packaged up in batches of five and output for shipment back to HQ (thus leaving the remainder when divided by five).

Matching Rule

Each Tacorama card lists a meal that can be made from a certain ratio of ingredients, shown in the top left corner of each. The ingredients are tortilla, cheese, and beef, going from top to bottom. On each card, the first present ingredient is the base and must be singular, and other ingredients are expressed in whole number increments relative to the first. Every card is unique and there are a total of 31 cards.

Every pair of two cards defines a recipe family of six cards. All of the recipes in a family can be made by different combinations of any two recipes from that family.

The Taco-Maker 5000 is limited to four helpings of each ingredient in a recipe; any combination of recipes that contains five or more helpings of any single ingredient will wrap back around to zero for that ingredient and then continue counting up. Note however that the ratios of ingredients must be simplified first, before determining any wrap-around to zero. Also note that the first ingredient present (in the order of tortilla, cheese, beef) must be expressed as one unit, with subsequent ingredients in whole-number increments thereof. If there are multiple of the base ingredient, you must scale the recipe until the base ingredient wraps back around to one.