The river crossing game solution

In the video, the narrator walks through this solution, but explains how it can be generalized by drawing up decision trees. At each step of the puzzle, you lay out all the possible options, then cross out any that don't work. As you proceed, the set of possibilities dwindle until you're left with only a few viable paths. The raft needs at least one animal to paddle it across the river, and it can hold at most two animals.

If the lions ever outnumber the wildebeest on either side of the river including the animals in the boat if it's on that side , they'll eat the wildebeest. Now we will make a graph with 10 nodes, where each node is one of the configurations above. Two nodes will be connected by an edge if and only if it is possible to get from one configuration to the other with a single boat trip.

Here, node 1 will be connected to node 6, and node 2 will be connected to node 7 and to node 8. We find that node 3 will be connected to three nodes; node 6, node 7, and node 9. Node 4 will be connected to node 8 and node 9, and node 5 will be connected to node 8 and node Going through the remaining nodes 6 - 10, we find no new connections the farmer has to return from the other river bank, resulting in one of the configurations 1 - 5.

The next step is to make a drawing of this graph. My computer abilities are very limited, but you should get something like this:. Finally, we return to the original question, which can now be interpreted as: Find a path in our graph starting at node 1 and ending at node The two solutions are immediately apparent!

You can't take the fox or the beans, and if you go solo you will come back solo and be back at the start. For the second move, if you take the goose back you are back where you started, so you come back solo. You are a long way into the puzzle by then. In most of these sorts of puzzles, there is a single moment when you crack it.

For this one, it's the realization that. I mean, that's kind of crazy, I am trying to get everything from this bank to that bank, why would I bring anything in the wrong direction? For the first step, you know it's ok to leave the fox with the beans, and it's not ok to leave the goose with anything, so you take it, fine.

Then whatever you take over next you're going to have to leave with the goose while you go back for the third thing, and that won't work. If taking the goose back occurs to you here, you've cracked the puzzle and the rest is just mechanics. Same thing with the limited-time lights and two-people-at-time-over-a-bridge thing.

Most people want to pair slow with fast, or put two slows together but the key to solving it is actually pairing the two fastest. With the liars and truth tellers it's asking one what the other would say. And so on. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Scan QR codes to connect to tons of digital content including video tutorials. Please login, or choose to sign-up, by clicking one of the buttons below.

Login Join. Scan QR codes to access exclusive digital content including video tutorials. We offer a range of membership plans with no surprises. Remember Me. Forgot Password. Don't have an account? Join Today. River Crossing 11 PDF. Team Puzzles 5 - 10 min Mini 1 — 7 Passive. Passive Develops critical thinking Fosters creativity Multiple variations No props. Save to Playlist. Step-by-Step Instructions Form small teams of 2 to 5 people. Challenge each team to solve an imaginary puzzle: Using a small rowboat, how can they transport a chicken, a fox and a bag of corn to the other side of the river in as few moves as possible.

To govern fair-play, the solution must acknowledge three critical parameters: — The rowboat can only carry one person and one item at any point in time. Describe the step-by-step solution to get all three items safely to the other side of the river. Allow ample time for discussion and trial-and-error. Allow ample time for your groups to discuss their ideas and perform lots of experiments.

Finally, she returns to pick up the chicken and rows across the river one last time. Jealous Partners River Crossing : Three married couples must cross a river using a boat which can hold two people maximum, subject to the constraint that no woman can be in the presence of another man unless her husband is also present. Bridge Crossing : Four people approach a narrow bridge crossing a river at night, but it can only hold two people at a time.

Each of the four people A, B, C and D travel at different speeds — 1, 2, 5 and 8 minutes respectively. Can all four people cross the river in 15 minutes or less?