Here are the six islands of Transumberg connected by nine bridges.
Can you find a route, starting on any of the islands, that crosses each bridge once?
If you found that puzzle easy try this:
Can you find a route crossing each bridge once (and only once)?
Which town is this?
How did you use this starter? Can you suggest
how teachers could present or develop this resource? Do you have any comments? It is always useful to receive
feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.
If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:
This starter has scored a mean of 3.2 out of 5 based on 254 votes.
Sign in to your Transum subscription account to see the answers
Can you make up your own bridge crossing puzzle with a different number of bridges and islands. How can you predict if the puzzle will be impossible?
Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.
Numbers and the Making of Us
I initially heard this book described on the Grammar Girl podcast and immediately went to find out more about it. I now have it on my Christmas present wish list and am looking forward to receiving a copy (hint!).
"Caleb Everett provides a fascinating account of the development of human numeracy, from innate abilities to the complexities of agricultural and trading societies, all viewed against the general background of human cultural evolution. He successfully draws together insights from linguistics, cognitive psychology, anthropology, and archaeology in a way that is accessible to the general reader as well as to specialists." more...
Teacher, do your students have
access to computers?
Here a concise URL for a version of this page without the comments.
Here is the URL which will take them to a similar type of puzzle.
"Here, my worthy Pilgrims, is a strange riddle," quoth the Parson. "Behold how at the branching of the river is an island. Upon this island doth stand my own poor parsonage, and ye may all see the whereabouts of the village church. Mark ye, also, that there be eight bridges and no more over the river in my parish. On my way to church it is my wont to visit sundry of my flock, and in the doing thereof I do pass over every one of the eight bridges once and no more. Can any of ye find the path, after this manner, from the house to the church, without going out of the parish? Nay, nay, my friends, I do never cross the river in any boat, neither by swimming nor wading, nor do I go underground like unto the mole, nor fly in the air as doth the eagle; but only pass over by the[Pg 49] bridges." There is a way in which the Parson might have made this curious journey. Can the reader discover it? At first it seems impossible, but the conditions offer a loophole.
The Canterbury Puzzles, by Henry Ernest Dudeney
In the history of mathematics, the first person go on record with a proven statement about the second problem above was Leonhard Euler in 1736. His 'solution' is considered to be the first theorem of graph theory and the first true proof in the theory of networks, a subject now generally regarded as a branch of combinatorics.
In addition, Euler's recognition that the key information was the number of bridges and the list of their endpoints (rather than their exact positions) is the basis of topology. The difference between the actual layout and the graph schematic is a good example of the idea that topology is not concerned with the rigid shape of objects.