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April 11th, 2018, 09:58 AM   #11
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Joined: Jun 2017
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Math Focus: Calculus

Originally Posted by skipjack View Post
Those three remaining circles that total 9 are the orange shaded circle, whose number I called x, and two other circles, whose numbers have a total I called y. Hence x + y = 9.

There are two arrowed rows of three (whose numbers therefore total 18 in each row) that include the orange shaded circle. These two rows contain the orange shaded circle twice and four other circles. I used z for the total of the numbers in those four other circles, so that 2x + z = 18 + 18.

The four circles that contributed towards z and the two circles that contributed towards y form, when considered together, two arrowed rows of three circles, so their numbers total 18 + 18, which means that y + z = 18 + 18. As 2x + z = 18 + 18 is already known, it follows that y = 2x. As x + y = 9, it now follows that x + 2x = 9, which implies that x = 3.
It took me a while to understand what you did but I'm still stuck at the part where you say "the two circles that contributed towards y form when considered together, two arrowed rows of three circles... $x+z=18+18$".

I thought that the four circles which surround the orange one would sum together 18. Is this part right?. I mean the ones which you say contributes towards z. As a pair is like to say their value is 9, as there are two pairs that is 18.

But the remaining ones I mean y which is one pair is only 9. Wouldn't it be from this y+z=18+9?. Can you explain this part a little bit better.

By trying again to understand then I thought that one straight line which contains orange circle is 18, the other two circles from the crossing line which forms the cross must be 9, so by sum is 27, but as there are another two which came y then those with the existing 27 must be 36, hence becoming the 18+18 you mentioned, but I don't know if this is what you implied. Moreover from this I imagine x+z+y=36. Sorry, I'm slow with these things.
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