| Related Puzzles
Allen was reading stories from Greek mythology and was fascinated by the story of
Theseus and the Minotaur. In this story Theseus goes into the labyrinth to find a monster
called the minotaur and must find his way out again. He unrolls a ball of string as he goes in
and follows it out after he has killed the minotaur. Allen decided to pretend that his house is the
labyrinth, and he is Theseus unrolling the string. He starts in the front door with his string. He wants
to make the most efficient search through his labyrinth, and go only once through each doorway. Can he
do it? What path should he follow? Here's the floor plan for his house:
Question: what are the bridges in this puzzle?
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THE BRIDGES OF KOENIGSBURG
 The famous Swiss mathematician Leonhard Euler
was visiting the city of Koenigsberg in Prussia in the year 1735. A favorite pastime for visitors
to the city was to try to solve this puzzle:
"Can you cross each of the bridges of Koenigsberg exactly once?"
Mr. Euler was told by some people that it was impossible and by others
that they doubted whether or not it could be done. No one believed it was possible.
Mr. Euler found a way to answer this question and settle everyone's doubts.
The geography:
The river Pregel goes through the city of Koenigsberg. There are two islands in the middle of the river, with 7 bridges connecting the islands to each other and to the banks of the river.
(Today Koenigsberg is part of Russia and is renamed Kaliningrad.)
Can you walk the 7 bridges of Koenigsberg, each exactly once?
This diagram can help you discover how Mr. Euler answered this question once and for all.
Here are a few more things to try:
If the Shopkeeper's Bridge burned down, would you be able to walk all 6 remaining bridges exactly once?
If the Green Bridge burned down instead, would you be able to walk all 6 remaining bridges exactly once?
If you built a new bridge from the upper bank to Kneiphof Island, would you be able to walk all 8 bridges exactly once?
Hint: Can you find a pattern in the numbers of bridges which lead to one of the four regions and whether or not you can walk the bridges? |
Related Puzzles
Genie was flying to visit several of her aunts and uncles over Christmas. She was flying on an airline with a
hub in Chicago and a hub in Denver. She had to get to Minneapolis to see her Aunt Minnie and to St. Louis to
see her Uncle Louis and to Little Rock to see her Uncle Rocco. Here's a picture of the flight paths for this airline:
Can Genie fly on each flight path exactly once and end up back in her own city of Eugene, OR?
Can she do it if she skips the trip to Little Rock?
Mike had had a very successful Cub Scout popcorn sale. Now the popcorn had arrived and it was time to deliver it to
all the neighbors. He had managed to sell popcorn to just about every household in his neighborhood and now had
to haul his load of popcorn along 22 blocks to deliver it. He's looking for the most efficient route through his
neighborhood--he wants to walk each block exactly once until all his popcorn is delivered. Can
you find a route for him? Here's a map of his neighborhood:
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