Hard Riddle #1 • page 6/6 • Off-Topic Discussion • lichess.org

@Nomen-Nonatur #46, so more rigorously:
Form the t meters of material into 2(pi)t/(t+1) degrees of a circle, and then insert the last meter of material to form a new circle with t+1 meters of material. I guess that would be one way of explaining it, since a circle has 2(pi) degrees.

@Nomen-Nonatur #46, so more rigorously: Form the t meters of material into 2(pi)t/(t+1) degrees of a circle, and then insert the last meter of material to form a new circle with t+1 meters of material. I guess that would be one way of explaining it, since a circle has 2(pi) degrees.

kyanite111

#52

Just in case anyone is interested, I found the "solution manual" to this problem, although I don't think it considers the case of an expanding circle either like ChessMath noted. It instead treats the problem as a linear rope that uniformly expands.

https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope

I think the harmonic series solution is the coolest. Bummed that I couldn't solve it correctly but oh well.

Just in case anyone is interested, I found the "solution manual" to this problem, although I don't think it considers the case of an expanding circle either like ChessMath noted. It instead treats the problem as a linear rope that uniformly expands. https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope I think the harmonic series solution is the coolest. Bummed that I couldn't solve it correctly but oh well.

Toscani

edited

#53

The rubber band circumference of 1 meter is growing at a rate of 1m/s.
The X starting point is somewhere on that circumference.
The robot starts the race at point X.
The robot's capable velocity is: 0.5 m/s
All they did was describe it's capabilities of the robot and the riddle is the if it would move.

But the concluding question was: Does !! ... the robot ever reach point x ever again?
Well if it was told to leave point X, then it never will reach it again, if it continues in the same direction. The circumference is expanding 2x faster than the speed of the robot.

But did the robot leave point X. No it did not leave point X. It was an if statement. The robot needs to go faster than the expansion to complete full circle in one direction. If it turns around, then it will be able to return to the starting point. The X will then be moving towards the robot as the robot moves towards the X.

The rubber band circumference of 1 meter is growing at a rate of 1m/s. The X starting point is somewhere on that circumference. The robot starts the race at point X. The robot's capable velocity is: 0.5 m/s All they did was describe it's capabilities of the robot and the riddle is the if it would move. But the concluding question was: Does !! ... the robot ever reach point x ever again? Well if it was told to leave point X, then it never will reach it again, if it continues in the same direction. The circumference is expanding 2x faster than the speed of the robot. But did the robot leave point X. No it did not leave point X. It was an if statement. The robot needs to go faster than the expansion to complete full circle in one direction. If it turns around, then it will be able to return to the starting point. The X will then be moving towards the robot as the robot moves towards the X.

Akbar2thegreat

#54

@kyanite111
Thanks for the link and as always my belief in Wikipedia never lets me down!

@kyanite111 Thanks for the link and as always my belief in Wikipedia never lets me down!