```ts
/** Replay tile requests against a size-limited cache of fresh renders. */
export function tileRenders(requests: [number, string][], freshFor: number, size: number): [number, string][] {
  if (!Number.isInteger(freshFor) || freshFor < 1 || !Number.isInteger(size) || size < 1) {
    throw new Error("freshFor and size must be positive integers");
  }
  const held = new Map<string, { tick: number }>();
  const renders: [number, string][] = [];
  for (const [tick, name] of requests) {
    if (held.has(name)) {
      const entry = held.get(name)!;
      if (entry.tick + freshFor > tick) {
        renders.push([tick, name]);
        continue;
      }
    }
    // Cache is not already holding the tile or it's too old to be used
    if (held.size === size) {
      const oldestEntry = Array.from(held.entries()).reduce((prev, curr) => prev.tick < curr[1].tick ? prev : curr);
      held.delete(oldestEntry[0]);
    }
    held.set(name, { tick });
    renders.push([tick, name]);
  }
  return renders;
}
```