Read the original question here
Answer: The total length of the four lines is 19 centimetres.
The winner is Josie Huddleston of Durham, UK. There were 172 entries.
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Worked answer
Starting with the simpler problem of dividing a circle with four radii so that cutting along two of the radii will produce two parts each equal in area to a multiple of 1/12 or the total area, we have the solution shown (see Fig 1, right).
As the area of the card is 72 square centimetres, the 4 areas defined by the 4 lines will be 6, 12, 18 and 36 cm2.
As the 4 lines radiate from the centre, at least one cannot be vertical or horizontal.
As the lengths of the lines are whole numbers of centimetres, the angle of at least one line must be one of the angles of a 3 – 4 – 5 triangle.
Only a little trial and error is needed to position the 3 – 4 – 5 triangle. The final result is shown in Fig 2, right.
The total length of the 4 lines is 19 cm.
