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The Foxes And Geese

Make a diagram of any convenient size similar to that shown in our illustration, and provide six counters—three marked to represent foxes and three to represent geese. 
Place the geese on the discs 1, 2, and 3, and the foxes on the discs numbered 10, 11, and 12

Now the puzzle is this. 
By moving one at a time, fox and goose alternately, along a straight line from one disc to the next one, try to get the foxes on 1, 2, and 3, and the geese on 10, 11, and 12—that is, make them exchange places—in the fewest possible moves.

But you must be careful never to let a fox and goose get within reach of each other, or there will be trouble. 
This rule, you will find, prevents you moving the fox from 11 on the first move, as on either 4 or 6 he would be within reach of a goose. 
It also prevents your moving a fox from 10 to 9, or from 12 to 7. If you play 10 to 5, then your next move may be 2 to 9 with a goose, which you could not have played if the fox had not previously gone from 10. 
It is perhaps unnecessary to say that only one fox or one goose can be on a disc at the same time. 
Now, what is the smallest number of moves necessary to make the foxes and geese change places?

See answer



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