Along the way there are 5 hiding places, one every 4 kilometers. These are the only places that they can safely stop to rest and eat. Each hiding place is so small that only one person can occupy it at a time, but a monk can stay there as long as desired. For religious reasons, a monk can enter or leave one of these hiding places, or reach the end of the trail, only on the exact hour. It is unsafe for any monk to stop and wait anywhere other than inside the hiding places or at the ends of the trail.
Because the trail passes through narrow gorges and dense forest it will be dark the entire time they are traveling, and because the trail is so narrow and steep they must use a light to keep from falling off. They have one large torch that two people walking together can use, and they have 9 candles that a single person can use. The torch is lit when they start, and will last 24 hours, but the candles last for only one hour each. The lama, the senior monk, who is the slowest walker, carries the torch and all of the candles. He will give the other monks only one candle at a time, and only at the start or at the hiding places.
What is shortest possible combined transit time for the four monks?
