Here are the rules.
A farmer wants to successfully ferry a fox, chicken, and sack of grain across a river. He can take several trips back and forth, drop things off, and pick things up on each side of the river between trips. But he can carry only two things in his small boat, other than himself, at one time.
Unfortunately, the farmer has a few problems.
If left alone together on the same side of the river, the fox will eat the chicken, and likewise, the chicken will eat the grain. But the fox will not eat the grain (and, of course, the chicken will not eat the fox).
How to get everything safely across the river?
I usually use coins of different sizes to represent the fox, chicken and grain, and a small torn piece of paper as the boat (rowed by the farmer).
It helps to use a sheet of paper with a "river" drawn on it to simulate the situation. You an download a printout here.
Similarly, there's a puzzle called "Cannibals and Missionaries," in which three missionaries are trying to get themselves across a river filled with man-eating fish. They have to contend with three cannibals, as well, who also must get across the same river in the same canoe at the same time.
Here are the conditions:
Only two people can occupy the boat, and multiple trips can be taken in either direction. People can get off the boat, once it gets to one side of the river or the other, and can re-enter the boat, at will. Unfortunately, if the cannibals outnumber the missionaries at any time on either side of the river, they will eat the missionaries. If this happens, the games ends unsuccessfully.
Complicating matters, only one missionary knows how to paddle the canoe, although all the cannibals know how to do so.
How to get all six people across the river in one piece?
In this case, I use three coins of one type to represent the missionaries (only one of which is heads up, indicating he can paddle the canoe), and three of another type as the cannibals.
Likewise, it helps to have the piranha-infested river drawn on a sheet of paper as a backdrop for the game, and a small piece of torn paper to use as the boat. Click here to download the backdrop.
In both games, the analogy to mathematics is found in the fact that, at each and every stage of the game, only one move makes sense and isn't obviously problematic. Patient, mindful examination of each potential move at each decision point leads one inevitably in the right direction – just as it does in solving math problems.
Can you do it? Give these a try!
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