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jasen

Equal product of dots in Hexagon

Question

Put number 2,3,5,6,10,12,15,18,20,45,50, and 75 to each line in the picture, so the product of lines which meet in every dot are equal.

A*L*H*B = B*G*I*C = C*H*J*D = D*I*K*E = E*J*L*F = F*K*G*A

if rotation and reflection are considered as 1 same solution, There are 16 solutions.

Untitled-2.png

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Spoiler

For what it's worth, if rotation and reflection are NOT considered one solution, then there are 196 answers...

Also, interestingly, all solutions have a product of 27,000.

Here's one configuration that works:

a=2, b=6, c=3, d=15, e=5, f=10, g=75, h=50, i=20, j=12, k=18, l=45

 

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