Enigma 1569 - Cardiology
Chappy
New Scientist magazine, 28 October 2009.
By Bob Walker.
Joe gave Penny a rectangular piece of card
12 centimetres by 8 centimetres with the
instruction that she had to draw two
intersecting straight lines across the card
from adjacent corners. The point of
intersection had to be such that by cutting
along two of the lines from the intersection
point to the edge of the card, a piece of
card with an area equal to any multiple
(from 1 to 6) of 8 square centimetres could
be produced.
How far from the nearer shorter side was the
point of intersection of the two lines?
Ciao,
Chappy.
Ilan Mayer
SPOILER
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Draw one line diagonally from corner to corner. Draw the other line
from the corner adjacent along the short edge to the centre of the
opposite long edge (see illustration).
+-------------+
| /|
| / |
| 40 / |
| / |
| / |
| / |
|\_ / 32 |
| \_ / |
| +_ |
| 8 / \_ |
| / \_ |
| / 16 \_ |
|/ \|
+-------------+
The areas in square centimetres are shown.
If the bottom left corner is at (0, 0), then the two lines are y =
1.5*x and y = 6-0.75*x. The intersection point is where 1.5*x =
0.75*x, and so it is (2 2/3, 4). This also confirms that the areas are
as indicated.
The point of intersection is thus 4 centimetres from the shorter side.
Please reply to ilan dot mayer at hotmail dot com
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\ /
__/\\ //\__ Ilan Mayer
\ /
/__ __\ Toronto, Canada
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Zurab57
> Enigma 1569 - Cardiology
> New Scientist magazine, 28 October 2009.
> By Bob Walker.
>
> Joe gave Penny a rectangular piece of card
> 12 centimetres by 8 centimetres with the
> instruction that she had to draw two
> intersecting straight lines across the card
> from adjacent corners. The point of
> intersection had to be such that by cutting
> along two of the lines from the intersection
> point to the edge of the card, a piece of
> card with an area equal to any multiple
> (from 1 to 6) of 8 square centimetres could
> be produced.
>