Yup. Assume a Cartesian plane (0, 0) and put teacher on (-1, 1) like shown above. Student will escape at (x, -1) [swim down]. Distance for teacher to get there is. is 2 + (1+x). Travel down and then travel right. Distance for student is sqrt(x^2 + 1). Teacher runs at 3t/sec.
Fun puzzle: A student is in the center of a square pool, the teacher at the corner. Teacher runs 3x as fast as student swims, but the student runs faster than the teacher. Can the student escape? (i.e. leave pool, never in the same location as the teacher, even for an instant)pic.twitter.com/Owwbb53ZGx
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Where t/sec is how a student moves. P1: So time for teacher to reach point: (3+x)/3t P2: And time for student to teach this point: sqrt(x^2 + 1)/t For student to get out: P2 > P1 Remember 0 < x < 1 (4th quadrant escape) Easy solution is (0.5, -1)
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Here's Numberphile doing it but with a circular pool.https://www.youtube.com/watch?v=vF_-ob9vseM …
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Easy! The teacher gets kicked out for running at the pool.
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I'm guessing yes, because going horizontally to the side in the image means they arrive at the edge at equal time (Swims half a length or 0.5L , teacher runs 1.5L) If, however, he swims diagonally, the teacher is forced to choose a side, so he can just go horizontal when he does)
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But go horizontal in the opposing direction. e.g.: Student swim to Right-Bottom corner -> 2 cases 1: Teacher goes down, Swim directly to the right 2: Teacher goes right, Swim directly down But Im likely wrong somwhere, I was too lazy to get pen and paper
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Yes the student can escape. If they were to go right then immediately down as the teacher follows, they will be one unit away from the bottom edge, but the teacher will be > 3 units away from the edge where they escape.pic.twitter.com/4xPTeYHtMA
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I thought this too, but after drawing it, the math doesn't check out. They both get there at the same time, but the student only escapes if they get there firstpic.twitter.com/1MovHybBHd
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I feel like by zig-zagging very slowly to the right you can actually keep the teaching on the left side of the pool.
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Yes, easily. Step 1: Nerd-snipe the teacher (see XKCD 356 and use a 3b1b tweet for bonus points) Step 2: While the teacher is thus disabled, casually leave the pool at leisure.
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Čini se da učitavanje traje već neko vrijeme.
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