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 Well Balanced Letter: F (Posted on 2007-05-16)
A letter F is composed of 6 unit squares and two rectangles of unit width as in the figure:

 X
Find the lengths of the two rectangles such that the center of gravity is at the center of the middle square.

 No Solution Yet Submitted by Jer Rating: 4.0000 (3 votes)

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 Well Balanced F Extension Comment 7 of 7 |

The big F below is a generalization of the original F.  Rectangles A and B are 1 by 1 squares.  Rectangles C and D are 1 by x.  Rectangle E is 1 by y.  Rectangle F is 1 by z.

`+----------------+| A|      E      |+--+-------------+|  || C||  |+--+-----+| B|  D  |+--+-----+|  ||  ||  || F||  ||  |+--+`

Like the original, the big F is to have its center of gravity at the center of rectangle D.

Solving for this F is just like the original F, just more variables.  Remarkably the lengths of y and z are both equal to (2x + 1 + sqrt[8x^2 + 16x + 9])/2

 Posted by Brian Smith on 2009-02-10 13:23:14

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