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Sunday Times Teaser 2558 – Round Table

by Brian Gladman on May 11, 2016

by H Bradley and C Higgins

Published: 2 October 2011 (link)

Pat likes to demonstrate his favourite trick shot on the pub pool table, which is 90in long and 48in wide.

Pat hits the ball so that it strikes the long side of the table first, then (after a perfect bounce) it hits the short side, then the other long side, and then finally the other short side, from which it returns to the starting point, making its path the perimeter of a quadrilateral.

What is the length of the perimeter of that quadrilateral?

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  1. Brian Gladman permalink

    st2558

    No program for this one since the analysis leaves nothing to be done. The table and the path of the ball is shown in the upper right of the diagram. By ‘reflecting’ the path in the sides of the table as shown, the path of the ball can be seen to be of the same length as that of the straight line path between the two dots. This can be seen by inspection to be double the height and width of the table itself.

    Hence the length of the path travelled by the ball is given by \[2\sqrt{w^2+h^2}\]. In our case this becomes \[2\sqrt{48^2+90^2}=12\sqrt{8^2+15^2}\] This is easily recognised as the Pythagorean triple \((8, 15, 17)\), which shows that the path length is 204cm.

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