**From New Scientist #2719, 1st August 2009** [link]

Joe gave Penny a rectangular piece of card 12 centimetres by 6 centimetres with the instruction that she had to draw four straight lines out from the centre of the card to an edge, each a whole number of centimetres long, so that, by cutting along two of the lines, a piece of card with an area equal to any multiple of 6 square centimetres (from 1 to 6) can be produced.

What will the total length of the four lines be?

[enigma1556]

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I initially solved this one by drawing it out, doing it programatically is a bit trickier, although it does find another family of answers (which give the solution).

The following Python program runs in 37ms.

Solution:The total length of the 4 lines is 19 cm.This is the solution I came up with on paper.

Cuts along the following 2 lines partition the rectangle into pieces with the following areas:

AB 6 + 66

BC 12 + 60

AC 18 + 54

CD 24 + 48

AD 30 + 42

BD 36 + 36

Of course there are answers that are rotations/reflections of this that give the same solution.

My program also found a second family of answers. The four lines are the same, but in a different configuration.

Cuts along the following 2 lines partition the rectangle into pieces with the following areas:

AB 6 + 66

CD 12 + 60

AC 18 + 54

BC 24 + 48

AD 30 + 42

BD 36 + 36