1. Konigsberg Bridge Problem

2. Konigsberg is now known as Kaliningrad, Russia

3. Konigsberg Bridge Problem

4. Konigsberg Bridge Problem

5. Konigsberg Bridge Problem

6. A popular puzzle of the day was this:
Is is possible to walk through Konigsberg and cross every bridge exactly once?

7. 1736: Leonhard Euler Proved that such a walk is impossible
1736: Leonhard Euler Proved that such a walk is impossible. In doing so, he was the first person to make use of Vertex-Edge Graphs.

8. Konigsberg Bridge Problem

9. The town can be drawn like this.

10. The town can be drawn like this.

11. The town can be drawn like this.

12. Each vertex is a landmass. Each edge is a bridge.

13. Euler’s insight:
While walking through Konigsberg, each time you visit one of the landmasses, you use up two of the bridges.

14. Euler’s insight:

15. Euler’s insight:

16. Euler’s insight:

17. Euler’s insight:

18. Euler’s insight:

19. Euler’s insight:

20. Euler’s insight:

21. Euler’s insight:

22. Euler’s insight:

23. Euler’s insight:

24. Euler’s insight:

25. Euler’s insight:

26. Euler’s insight:
If a landmass/vertex has an odd number of bridges/edges, you must start or end on it.
If you have more than two vertices with an odd number of edges, then it is impossible!
If you have zero or two, then it is always possible.

27. 3 5 3 3
This has 4 odd vertices, so it is impossible.

32. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com

33. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com

34. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com

35. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com

36. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com

37. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com

38. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com

39. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com

40. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com

41. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com

42. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com

43. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com

44. Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com