Interstellar Basic Algebra
by Ken Stern and Ian Tullis
Answer: SOBER UP
These pictures represent the names of different mixed drinks. In order, they are: Americano, Black Russian, Brandy Alexander, Bronx, French Connection, Gibson, Godmother, Golden Cadillac, Harvey Wallbanger, Mimosa, Negroni, Screwdriver, White Russian. Each of these drinks has a standard International Bartenders Association recipe [1]; these also appear on the cocktails' Wikipedia pages. That is, Americano = 3 cl Campari + 3 cl Sweet Red Vermouth, etc. The recipes for these 13 cocktails involve a total of 13 ingredients, and they can be treated as a linear system of 13 equations in 13 unknowns.
| Unknown | Ingredient | Americano | Black Russian | Brandy Alexander | Bronx | French Connection | Gibson | Godmother | Golden Cadillac | Harvey Wallbanger | Mimosa | Negroni | Screwdriver | White Russian |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| a | Amaretto | 0 | 0 | 0 | 0 | 3.5 | 0 | 3.5 | 0 | 0 | 0 | 0 | 0 | 0 |
| b | Campari | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 0 | 0 |
| c | Champagne | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 7.5 | 0 | 0 | 0 |
| d | Coffee Liqueur | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 |
| e | Cognac | 0 | 0 | 2 | 0 | 3.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| f | Crème de Cacao | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 |
| g | Dry Vermouth | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| h | Fresh Cream | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 3 |
| i | Gin | 0 | 0 | 0 | 3 | 0 | 6 | 0 | 0 | 0 | 0 | 3 | 0 | 0 |
| j | Liquore Galliano | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 1.5 | 0 | 0 | 0 | 0 |
| k | Orange Juice | 0 | 0 | 0 | 1.5 | 0 | 0 | 0 | 0 | 9 | 7.5 | 0 | 10 | 0 |
| l | Sweet Red Vermouth | 3 | 0 | 0 | 1.5 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 0 | 0 |
| m | Vodka | 0 | 5 | 0 | 0 | 0 | 0 | 3.5 | 0 | 4.5 | 0 | 0 | 5 | 5 |
That is, this is the 13x13 matrix M that can be used to solve equations of the form Mx = y, where x is a 13x1 vector of numbers of drinks and y is a 13x1 vector of total amounts of each ingredient.
a, b, c, d, etc. are unit vectors for each of the ingredients. The first equation in this puzzle allows their identities to be confirmed; a turns out to be for Amaretto, b for Campari, etc. Once that's been determined, the second equation can be solved using some matrix algebra. We have Mx = y, with M and y given and x unknown. M is invertible, so x = (M-1)y = [1 14 19 23 5 18 19 15 2 5 18 21 16]. Indexing into the alphabet gives ANSWER SOBER UP, so SOBER UP is the answer to the puzzle.