Write the position down
A river crossing puzzle has fewer positions than it looks. A position is three things: who is on the near bank, who is on the far bank, and which bank the boat is touching. Nothing else matters, and the order people are standing in does not matter at all.
Write it as two lists and an arrow. Near: farmer, wolf, goat, cabbage. Far: nobody. Boat: near. That describes the start of the classic wolf, goat and cabbage puzzle.
Then list the pairs that cannot be left alone. The wolf and the goat. The goat and the cabbage. Both are fine while the farmer is standing there, so the only thing to check is the bank the farmer is leaving.
The practice also has boards with wizards and goblins, where the rule counts heads on each bank instead of naming pairs. Those are the puzzle older books call missionaries and cannibals.
Seven crossings, including bringing the goat back
Here are the seven crossings. The farmer rows every time.
Take the goat over. Come back alone. Take the wolf over. Bring the goat back. Take the cabbage over. Come back alone. Take the goat over.
The fourth crossing is the one people miss. It carries the goat the wrong way. Without it the wolf is left with the goat or the goat is left with the cabbage, and there is no way through.
That is the shape of almost every board here. Something has to come back, and working out what it is settles the whole answer.
The lantern crossing
One board counts minutes instead of crossings. Four walkers have one lantern between them. One or two can cross at a time with the lantern, a pair goes at the slower one's pace, and someone has to bring the lantern back.
The four walkers take 1, 2, 5 and 10 minutes. Sending the fastest walker with each of the others in turn costs 19 minutes. The answer is 17, and it comes from one idea: the two slowest walkers should cross together, so the slowest one's time is paid once and covers both.
This puzzle is also known as the bridge and torch puzzle, which is the same thing with a bridge instead of a boat.
Try it
In the lantern crossing, what do the two slowest walkers do?
- They cross together, so the slower one's time covers both
- They each cross with the fastest walker
Show the answer
They cross together, so the slower one's time covers both
Correct. 1 and 2 cross (2 minutes). 1 comes back (1). 5 and 10 cross together (10). 2 comes back (2). 1 and 2 cross (2). That is 17. The 5 and the 10 cost 10 minutes once, and a fast walker already on the far side brings the lantern back.
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Practice River crossing puzzles