Scary Decagon

Level pending

Let A B C D E F G H I J ABCDEFGHIJ be a regular decagon ( 10 10 -sided polygon). Extend A F AF to K K such that A F : F K = 2 : 1 AF:FK = 2:1 . Find the sum of the squares of the digits of K A ⋅ K B ⋅ K C ⋅ K D ⋅ K E ⋅ K G ⋅ K H ⋅ K I ⋅ K J K F 9 \dfrac{KA \cdot KB \cdot KC \cdot KD \cdot KE \cdot KG \cdot KH \cdot KI \cdot KJ}{KF^{9}}


The answer is 14.

Akshaj Kadaveru by Akshaj Kadaveru , 20, USA

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1 solution

Faraz Masroor
Dec 24, 2013

We'll uh I'm lucky this worked out... If we draw this in the plane the decagon is just the 10th roots of unity, the defining polynomial being x^10-1 which wen evaluated At K, 2, yields 1023->14. Although I am worried about the mag tide as we never used the fact that we need magnitude in the solution....?

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