The Apothecary's Bench

You are a colourman in a medieval workshop, and the guild has sent a docket. There are three pigments on the shelf — orpiment yellow, ultramarine blue, vermilion red — and eighteen colours that can be made from them. Not by choosing ingredients, but by measure. Four parts yellow to two parts blue is sap green. Three to one is reseda. One to one is verdigris. Get the proportion wrong and you have not made nothing; you have made something else, and the crate wanted the other thing. A pour fills the vessel it goes into, or empties the one it comes from, whichever happens first. You never choose an amount. Everything else follows from that. A HUNDRED AND TWO BENCHES, EVERY ONE SOLVED BY MACHINE Each level was solved by the game's own solver before it was allowed in. On ninety-nine of them the par beside it is the proven shortest solution; the other three are too large to search completely,…