Editing 2694: Königsberg
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[[Cueball]] attempts to cheat on the final exam in his algorithms class by traveling back in time to commission the construction of an eighth bridge before Euler could learn of the problem, allowing a trivial solution that would remove the rationale for further analysis. He hopes that this would alter his present-day timeline in such a way that the test becomes easier because graph theory might never have been developed. The use of the word "tried" implies failure, which is probably a good thing since his success would create a {{w|Temporal_paradox#Grandfather_paradox|paradox}}. [[:Category:Time travel|Time travel]] is a recurring topic on xkcd and examples where attempts to change the past fails has also been used before like in [[1063: Kill Hitler]]. | [[Cueball]] attempts to cheat on the final exam in his algorithms class by traveling back in time to commission the construction of an eighth bridge before Euler could learn of the problem, allowing a trivial solution that would remove the rationale for further analysis. He hopes that this would alter his present-day timeline in such a way that the test becomes easier because graph theory might never have been developed. The use of the word "tried" implies failure, which is probably a good thing since his success would create a {{w|Temporal_paradox#Grandfather_paradox|paradox}}. [[:Category:Time travel|Time travel]] is a recurring topic on xkcd and examples where attempts to change the past fails has also been used before like in [[1063: Kill Hitler]]. | ||
| − | With the addition of the eighth bridge, it becomes possible to cross each bridge exactly once, starting at the north bank and ending on the larger eastern island, or vice-versa. However, there is still no way to traverse each bridge exactly once and return to the starting point, because the altered graph would have an {{w|Eulerian trail|Euler trail}} but not an Euler cycle. Thus the problem might still have been interesting to Euler.{{Citation needed}} (Adding a ninth bridge connecting the north bank to the east island would render the problem completely trivial.) We can't say whether Euler or others would have developed graph theory anyway, or whether Cueball's exam would have been any easier | + | With the addition of the eighth bridge, it becomes possible to cross each bridge exactly once, starting at the north bank and ending on the larger eastern island, or vice-versa. However, there is still no way to traverse each bridge exactly once and return to the starting point, because the altered graph would have an {{w|Eulerian trail|Euler trail}} but not an Euler cycle. Thus the problem might still have been interesting to Euler.{{Citation needed}} (Adding a ninth bridge connecting the north bank to the east island would render the problem completely trivial.) We can't say whether Euler or others would have developed graph theory anyway, or whether Cueball's exam would have been any easier, more difficult, or similar. |
An alternative modification allowing an easy solution is to remove bridges. During World War II, two bridges to the central island connecting it to the north and south banks were destroyed by bombing, so today there is an Eulerian trail across the five remaining bridges. | An alternative modification allowing an easy solution is to remove bridges. During World War II, two bridges to the central island connecting it to the north and south banks were destroyed by bombing, so today there is an Eulerian trail across the five remaining bridges. | ||
