Spiked Math Games  // Math Fail Blog  // Gauss Facts  // Spiked Math Comics



Solutions to the Seven Bridges of Konigsberg - February 12, 2013
Rating: 4.7/5 (106 votes cast)
  • Currently 4.7/5
  • 1
  • 2
  • 3
  • 4
  • 5
Spiked Math Comic - Solutions to the Seven Bridges of Konigsberg

home     info     archive     contact     rss

Google+ Page   //   Facebook Page   //   Twitter Page


The physicist cheated. You can only use a bridge to get from one landmass to another, and she used a teleporter. DQ!

Possibly the physicist used an Einstein-Rosen bridge to teleport?

The physicist would of course use her wave properties in order to cross two bridges at the same time and then fuse together on the other side. It only works as long as no one is looking, though.

Mathematician's solution: assuming the land patches are divided by a river, that river must originate at some point, beyond which two of the land masses are connected. The remainder of the proof is left as an exercise for the student.

Brilliant!! You just made my day :)

This was actually a plot point in a murder mystery. The killer left the puzzle as a clue, and a building at the source of the river held the details of the crime.

Sadly the land masses are enclosed by forking rivers. So here's my solution instead:

When he said "crosses each bridge only once", I interpret that as "each [of the seven bridges previously mentioned] only once". But when he says "you may only travel between land masses by using a bridge", that includes any bridge, even those not previously mentioned. So simply follow one of the rivers upstream and cross a bridge other than the seven previously mentioned.

That's about the same as the engineers' solution.

Yes, but then you have an existence proof on your hands!

Geologist's solution: dry up a part of the river.

Or dump enough dirt to connect the left island to the land on one of the two sides of the river.

Dont give a shhit

Alternatively, the physicist could walk very quickly over one of the bridges and declare it ‘uncrossed with sufficient accuracy’.

The PE teacher's solution: Swim across the river.

I wonder how M.C. Escher would solve this quandary.

Walk on the underside of the bridges.

Philosopher's solution: The "same" bridge is actually a different bridge at a different point in time. Walk over "same" bridge twice.


The Politician's solution: lie about how many bridges were crossed

Evil Knievel's solution: use a motorcycle to jump one of the rivers

The Lawyer's solution: redefine "crossing" so it allows going part-way across a bridge and turning around

The Businessman/woman's solution: pay 7 people to each cross 1 bridge

Salvador Dali's solution: a mess of paths, some crossing the water

Your strip inspired my analysis of the modern Königsberg bridges:

Move the bridge.

Every river has headwaters right? You don't have to teleport or anything. Just go to the hill and round the river.

The Mythbusters solution actually got implemented during WW2. An Euler path in Königsberg/Kaliningrad is possible now.

So none of them can swim?

Leave a comment

Profile pictures are tied to your email address and can be set up at Gravatar. Click here for recent comments.
(Note: You must have javascript enabled to leave comments, otherwise you will get a comment submission error.)
If you make a mistake or the comment doesn't show up properly, email me and I'll gladly fix it :-).


home     info     archive     contact     rss

Google+ Page   //   Facebook Page   //   Twitter Page

Welcome to Spiked Math!

Hello my fellow math geeks. My name is Mike and I am the creator of Spiked Math Comics, a math comic dedicated to humor, educate and entertain the geek in you. Beware though, there might be some math involved :D

New to Spiked Math?
View the top comics.

New Feature: Browse the archives in quick view! Choose from a black, white or grey background.