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Morningstar

Question

I read about this in a Russian puzzle book and I don't think it's been posted before.

A soccer goalie had just lost an important match, and when he went to sleep that night he had a strange dream. He dreamt that he was kicking a soccer ball against a wall, and as he did so, the soccer ball got bigger and bigger, and the goalie got smaller and smaller. Suddenly, the goalie turned into a ping-pong (table tennis) ball and the soccer ball turned into a massive hard exercise ball. The exercise ball rolled around, trying to crush the ping-pong ball. Without leaving the floor, is there any way the ping-pong ball can prevent being crushed?

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This has to be one of the weirder contexts but alright...

...there was a wall, right? Couldn't he simply get into the corner (or inside of the edge made by the wall and floor? If the ping-pong ball was small enough or the exercise ball was large enough (or both), then it would work.

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Treat the balls as 2D circles: if the medicine ball is of diameter D and it is up against the wall, there will be a square around it, sides D. This means the diagonal of the square across it is root2*D. As such there is a gap either side of it, each of length (Root2/2 - .5)D and if the smaller ball's diameter is less than this it will fit up against the wall, where it cannot be crushed by the larger ball.

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<p>i agree with Faizaan and Assassinator,

another strategy:&nbsp; if the ping pong ball can find some sort of hole in the ground with depth = (height of ping pong ball), then it can find a safe haven.

</p>

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With no basis on math but rather experience, one answer could be for the keeper to wake up. With no dreaming there is no crushing of ping pong balls

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The standard medicine ball diameter is 14 inches; while standard ping pong ball diameter is 1.574 inches. The ping pong ball just has to roll close to the wall and will have plenty of room to spare so as not to be crushed. I graphed it visually using GeoGebra and will try to share the pic.

Edited by Fizzicks

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<p>i agree with Faizaan and Assassinator,

another strategy:&nbsp; if the ping pong ball can find some sort of hole in the ground with depth = (height of ping pong ball), then it can find a safe haven.

</p>

I like the thinking outside the box
WE have two problems, first, the depth of the hole would need to be greater than the height of the ball. Assuming the measurements given by Fizzicks are correct, then the medicine ball while over the hole will protrude into the hole .072 inches requiring additional depth. Second, the specifications of original problem was to not leave the floor and the ping pong ball in the hole would no longer be in contact with the floor.

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No need to assume there is a wall, the puzzle stated that the goalie was kicking against a wall.

Another solution: the ping pong ball could roll faster that the big ball and out run it.

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If the friction between the two balls is greater than that of the ping pong ball to the field, the larger medicine ball should simply push the ping pong ball around.

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sorry for being so picky but i don't think you can use a exercise ball to crush a ping pong ball without picking it up

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sorry for being so picky but i don't think you can use a exercise ball to crush a ping pong ball without picking it up

I don't know, exercise balls are pretty heavy. Why don't we try it? :)

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<p>

<br />

I like the thinking outside the box

WE have two problems, first, the depth of the hole would need to be greater than the height of the ball. Assuming the measurements given by Fizzicks are correct, then the medicine ball while over the hole will protrude into the hole .072 inches requiring additional depth. Second, the specifications of original problem was to not leave the floor and the ping pong ball in the hole would no longer be in contact with the floor.

<br />

</p>

<p>&nbsp;</p>

<p>You are correct in that the medicine ball would produde into the hole. However

instead of the ping pong ball navigating into a hole how about the terrain is such that there exists an area where the ping pong ball could prevent being squashed...think of bumpy terrain.( remember the Q does not specify where the balls are. it just says that there is a wall. )

</p>

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