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The sample problem I kind of gave up on and guessed sort of... it couldn't be sorted by color that's too obvious.

And then the real problem number 1. The answer is "Left - each figure contains an even number of arrow heads. Right - each figure contains an odd number of arrow heads"... but on the right I can clearly see that the three eggs across the top have an even number of arrowheads.

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It's not the number of arrowheads on the egg; it's the number of arrowheads on each of the little figures on the egg. Those eggs you mention have 2 figures each, true, but each figure has just 1 arrowhead each.
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If you have an Ultra subscription (I don't or I would try it) I would be really curious if Carbon is able to solve your harder Bongard problem without making stuff up given it's absurdly high AA Omniscience non-hallucination score, it's supposed to be like 30%+ better than nearest non-Google competitor. Although Hydrogen xhigh apparently scored within 5% of Carbon so who knows ¯\_(ツ)_/¯
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I don't have that subscription, but for the record, it's this problem: https://imgur.com/a/idyH0Kh

I won't share the solution (you have to keep some mystery in the world), but I showed this a year ago at a high-school reunion and five people independently found the same solution, so it should be well-posed.

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