4 ms·

My Cambridge interview tested for this explicitly. They gave you 45 minutes to prepare answers to 8 'further maths' type questions, then you had to solve some c

My Cambridge interview tested for this explicitly. They gave you 45 minutes to prepare answers to 8 'further maths' type questions, then you had to solve some creative problems at the end. These creative problems required knowledge of further maths concepts but were unusual so you needed time to think about them and develop a mathematical framework for the solution, this therefore tested that you could do the further maths questions easily and quickly and that you could solve new problems. The 'creative' problem I had was this: A mouse walks along an elastic band at 2 meters per minute. The elastic band stretches by 1 kilometer every hour. How far along the band does the mouse get? If you got that right, then they gave you a stretch question where the band doubles in length every hour.

cgio 11y ago
Am I wrong to think that the stretching of the band does not have anything to do with "how far along the band" the mouse will travel? Maybe it's my English as a second language, but my intuition is that the mouse still travels along the band as it expands, and you would probably need a point of reference, e.g. How far along the gap that the elastic band bridges to make the question more challenging.
- tfgg 11y ago
  The mouse is walking along the band, while the end of the band moves away, however the mouse is also being carried along by the expansion of the band. I think the best approach is to think in terms of the fractional coordinate of the mouse along the band, and work out its effective velocity in this coordinate.
  - technotony 11y ago
    Correct, if you structure the problem as the proportion completed at time t relative to the proportion at time t-1, then you can sum in the limit as t goes to infinity to show surprisingly that he gets to the end under both scenarios.
  - cgio 11y ago
    The elastic band could expand in both directions or either. If I assume the band expands so fast that I remain at the same point with regards to a point of reference, have I not still moved by 2m along the band after a minute? I guess it's more about the semantics of how moving along the band applies. Also how the expansion carries the mouse has to do with its movement. E.g. if it's galloping it would not carry it.
theoh 11y ago
I think you meant to say "if you got that right, then they gave you a stretch stretch question" :-)

cgio 11y ago

Am I wrong to think that the stretching of the band does not have anything to do with "how far along the band" the mouse will travel? Maybe it's my English as a second language, but my intuition is that the mouse still travels along the band as it expands, and you would probably need a point of reference, e.g. How far along the gap that the elastic band bridges to make the question more challenging.

tfgg 11y ago
The mouse is walking along the band, while the end of the band moves away, however the mouse is also being carried along by the expansion of the band. I think the best approach is to think in terms of the fractional coordinate of the mouse along the band, and work out its effective velocity in this coordinate.
- technotony 11y ago
  Correct, if you structure the problem as the proportion completed at time t relative to the proportion at time t-1, then you can sum in the limit as t goes to infinity to show surprisingly that he gets to the end under both scenarios.
- cgio 11y ago
  The elastic band could expand in both directions or either. If I assume the band expands so fast that I remain at the same point with regards to a point of reference, have I not still moved by 2m along the band after a minute? I guess it's more about the semantics of how moving along the band applies. Also how the expansion carries the mouse has to do with its movement. E.g. if it's galloping it would not carry it.

theoh 11y ago

I think you meant to say "if you got that right, then they gave you a stretch stretch question" :-)