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Equal product of dots in Hexagon



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.


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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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