Ball Jumping

A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?




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In the Mexico City area, there are two Houses H1 and H2. Both H1 and H2 have two children each.
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There was once a college that offered a class on probability applied to the real world. The class was relatively easy, but there was a catch. There were no homework assignments or tests, but there was a final exam that would have only one question on it. When everyone received the test paper it was a blank sheet of paper with a solitary question on it: 'What is the risk?'.Most students were able to pass, but only one student received 100% for the class! Even stranger was that he only wrote down one word!
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In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki