Re: Enigma 1513 - Two polygons

On Nov 12, 9:37 pm, Chappy <petergregorychap...@xxxxxxxxxxx> wrote:
Enigma 1513 - Two polygons
New Scientist magazine, 27 September 2008.
By Richard England.

I drew a regular polygon that had X sides
and a second regular polygon that had Y
sides.  Just as my second polygon had (Y-X)
more sides than my first polygon, so each
internal angle of the second polygon was
(Y-X) degrees greater than each internal
angle of my first polygon.  (X+Y) was a
perfect square.

How many sides did each of my polygons have?

Ciao,
Chappy.

SPOILER

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For n sides the angles are 180-360/n

Integer values:
n angle
3 60
4 90
5 108
6 120
8 135
9 140
10 144
12 150
15 156
18 160
20 162
24 165
30 168
36 170
40 171
45 172
60 174
72 175
90 176
120 177
180 178
360 179

The only pair from the table which meets the requirements:
9 140
40 171

Thus the polygons have 9 and 40 sides.



Please reply to ilan dot mayer at hotmail dot com

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__/\\ //\__ Ilan Mayer
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