Four People on a Rickety Bridge
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
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Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Four people need to cross a rickety bridge at night. Unfortunately they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: pqmin pqmin pqmin and pqmin. What is the shortest time needed for all four of them to cross the bridge?
Solution:
The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? + + + + pqmin Is that it? No. That would make this question too simple even as a warm up question. Let’s brainstorm a little further. To reduce the amount of time we should find a way for and to go together. If they cross together then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have one waiting on the other side to bring the torch back. Aha we are getting closer. The fastest way to get one across and be back is to use two to usher one across. So let’s put all this together. compactitem item and go cross item comes back item and go across item comes back item and go across done compactitem Total time: + + + + pqmin
Four people need to cross a rickety bridge at night. Unfortunately they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: pqmin pqmin pqmin and pqmin. What is the shortest time needed for all four of them to cross the bridge?
Solution:
The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? + + + + pqmin Is that it? No. That would make this question too simple even as a warm up question. Let’s brainstorm a little further. To reduce the amount of time we should find a way for and to go together. If they cross together then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have one waiting on the other side to bring the torch back. Aha we are getting closer. The fastest way to get one across and be back is to use two to usher one across. So let’s put all this together. compactitem item and go cross item comes back item and go across item comes back item and go across done compactitem Total time: + + + + pqmin
Meta Information
Exercise:
Four people need to cross a rickety bridge at night. Unfortunately they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: pqmin pqmin pqmin and pqmin. What is the shortest time needed for all four of them to cross the bridge?
Solution:
The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? + + + + pqmin Is that it? No. That would make this question too simple even as a warm up question. Let’s brainstorm a little further. To reduce the amount of time we should find a way for and to go together. If they cross together then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have one waiting on the other side to bring the torch back. Aha we are getting closer. The fastest way to get one across and be back is to use two to usher one across. So let’s put all this together. compactitem item and go cross item comes back item and go across item comes back item and go across done compactitem Total time: + + + + pqmin
Four people need to cross a rickety bridge at night. Unfortunately they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: pqmin pqmin pqmin and pqmin. What is the shortest time needed for all four of them to cross the bridge?
Solution:
The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? + + + + pqmin Is that it? No. That would make this question too simple even as a warm up question. Let’s brainstorm a little further. To reduce the amount of time we should find a way for and to go together. If they cross together then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have one waiting on the other side to bring the torch back. Aha we are getting closer. The fastest way to get one across and be back is to use two to usher one across. So let’s put all this together. compactitem item and go cross item comes back item and go across item comes back item and go across done compactitem Total time: + + + + pqmin
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