River Crossing Puzzles: Solutions

How the puzzles work

Everyone starts on the near bank. You put characters in the boat by tapping them, and someone who can row has to be aboard before it moves. When the boat lands, the rules are checked on both banks and in the boat that just crossed. A broken rule is shown at once, and Undo takes the crossing back. Getting everyone to the far side solves the puzzle, and doing it in the fewest crossings earns three stars.

Three habits solve most of them:

• The return trip is the trick. In almost every puzzle something has to go back the way it came. It feels like losing ground, but it is usually the key move.
• Check the bank you leave. A rule breaks just as easily behind the boat as in front of it.
• Work backwards. Picture the last crossing: who is in the boat, and who is already waiting on the far bank? That position is often easier to reach than it looks.

1. Wolf, Sheep and Cabbage

The farmer rows, and the boat takes him and one more. The wolf eats the sheep and the sheep eats the cabbage whenever the farmer is away. The sheep is the trouble: it clashes with both of the others, so it has to go first and it has to come back once.

1. Take the sheep over.
2. Row back alone.
3. Take the wolf over.
4. Bring the sheep back.
5. Take the cabbage over.
6. Row back alone.
7. Take the sheep over.

Seven crossings. Swapping the wolf and the cabbage in steps 3 and 5 works just as well.

2. Two Children and Two Grown-ups

The boat holds both children or one grown-up. Each grown-up costs four crossings: both children go over, one comes back, the grown-up goes over, and the other child brings the boat back. Do that twice, then the children cross together at the end.

1. Both children over.
2. One child back.
3. The first grown-up over.
4. The other child back.
5. Both children over.
6. One child back.
7. The second grown-up over.
8. The other child back.
9. Both children over.

Nine crossings, and every one of them is needed.

3. The Night Bridge

The hikers take 1, 2, 5 and 10 minutes, two cross at a time at the slower pace, and the torch has to come back each time. The obvious plan is to let the fastest hiker walk everyone over and carry the torch back, which takes 19 minutes. The best plan sends the two slowest hikers together, so their long walk is only counted once.

1. 1 and 2 cross: 2 minutes.
2. 1 brings the torch back: 1 minute.
3. 5 and 10 cross: 10 minutes.
4. 2 brings the torch back: 2 minutes.
5. 1 and 2 cross: 2 minutes.

That is 17 minutes, the fewest possible.

4. Shepherds and Wolves

Three shepherds and three wolves, a boat for two, and the wolves may never outnumber the shepherds on a bank where there are shepherds. A bank with only wolves is safe, and that is the idea to hold on to: move the wolves over first, then the shepherds, with one shepherd and one wolf crossing back together in the middle.

1. A shepherd and a wolf over.
2. The shepherd back.
3. Two wolves over.
4. One wolf back.
5. Two shepherds over.
6. A shepherd and a wolf back.
7. Two shepherds over.
8. A wolf back.
9. Two wolves over.
10. A shepherd back.
11. The shepherd and the last wolf over.

Eleven crossings. Step 6 is the one most players miss.

5. Knights and Squires

Three knights, their three squires, and a boat for two. A squire may not be with another knight unless their own knight is there too, on a bank or in the boat. The plan is the same shape as the shepherds: squires first, then knights, with one pair coming back together.

1. The red knight and squire over.
2. The red knight back.
3. The blue and green squires over.
4. The red squire back.
5. The blue and green knights over.
6. The blue knight and squire back.
7. The red and blue knights over.
8. The green squire back.
9. The red and blue squires over.
10. The green knight back.
11. The green knight and squire over.

Eleven crossings. Any colours will do, as long as each pair keeps to the rule.

6. Four Shepherds, Four Wolves

With four of each the old boat of two cannot do it, but a boat of three can, in nine crossings. Two shepherds and a wolf go over together, a shepherd and a wolf come back, and then three shepherds cross at once.

1. A shepherd and a wolf over.
2. The shepherd back.
3. Two shepherds and a wolf over.
4. A shepherd and a wolf back.
5. Three shepherds over.
6. A wolf back.
7. Two wolves over.
8. A wolf back.
9. Three wolves over.

7. The Family Raft

The hardest of the seven: father, mother, two sons, two daughters, a guard and a thief, a raft for two, and only the father, the mother and the guard can steer. The father may not be with a daughter without the mother, the mother may not be with a son without the father, and the thief may not be with any of the family without the guard. The guard and the thief move as a team, and the sons cross before the daughters.

1. Guard and thief over.
2. Guard back.
3. Guard and a son over.
4. Guard and thief back.
5. Father and the other son over.
6. Father back.
7. Father and mother over.
8. Mother back.
9. Guard and thief over.
10. Father back.
11. Father and mother over.
12. Mother back.
13. Mother and a daughter over.
14. Guard and thief back.
15. Guard and the other daughter over.
16. Guard back.
17. Guard and thief over.

Seventeen crossings, and there is no shorter way.

A very old kind of puzzle

The farmer with a wolf, a goat and a cabbage appears in a collection of puzzles for young people put together around the year 800, along with a crossing for three men and their sisters, the ancestor of the knights and squires. The shepherds and wolves came later, and the night bridge with its single torch is a twentieth century puzzle. The family raft is younger still. They have lasted because they are easy to state and teach a real habit: listing what can happen, ruling out what must not, and noticing that the step that looks backwards is often the one that solves it.