Three or four roommates, the same number of rooms, one rent. Each dot on the triangle (or tetrahedron, for four) is one way to split the rent, and the person who owns that dot says which room they'd take at those prices. Sperner's lemma guarantees a small cell where everyone picks a different room. That cell is an envy-free split.
Each person's final price is within one step of a price at which they said they wanted that room. A coarse grid is fast but leaves more room for "I'd rather have hers at that price." A fine grid is fairer but asks more questions.
Start with Standard. If anyone feels the result is off, start a Fine session and answer again. For a large rent, where one step is hundreds, go Very fine, or let each person enter room values and have the page answer for them.
Every question assumes a free room beats any paid room. Answer only on the prices shown, not on what the others might pick. The math does the coordinating.