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2 possible methods

Are cylindrical casts allowed?

The solutions above seem to be for the first 5 eggs. I understood that it was any 5 eggs out of the 12. Try this then!

Nice Witzar. I had another approach which was to consider any expected dot rather than only 6...

I don't understand this solution. What is Bi? Bi is a blue ball at position i (i is from 1 to 10). For the tenth ball bi is blue ball 10 and Bi+1 is blue ball 1

Come to think of it...

But weight difference is always positive. Yes, that is why we sort them into two piles depending on whether the next ball is heavier or lighter. And the two piles would weigh the same

Ah the editor did not let me change the formatting while editing. In the previous post, I copy pasted from excel. While editing it showed things fine but the final result was all messed up as you can see in the previous post. This should look better Otherwise Weigh 2 4 6 8 10 12 It should weigh 42 If it weighs other than 42, refer to weighings "B" below - max 3 more weighings needed Otherwise Weigh 1 2 11 12 It should weigh 26 If it weighs other than 42, refer to weighings "C" below Otherwise Weigh 3 4 10 It should weigh 17 If it weighs 17, then eggs 7 &9 are swapped If it weighs (-2) 15, then eggs 8 & 10 are swapped Otherwise, it weighs 19 (+2) and the possibilites are 3&5 or 4&6 are swapped Weigh 3 If it weighs 5, then eggs 3 & 5 are swapped Otherwise eggs 4 & 6 are swapped

Otherwise Weigh 2 4 6 8 10 12 It should weigh 42 If it weighs other than 42, refer to weighings "B" below - max 3 more weighings needed Otherwise Weigh 1 2 11 12 It should weigh 26 If it weighs other than 42, refer to weighings "C" below Otherwise Weigh 3 4 10 It should weigh 17 If it weighs 17, then eggs 7 &9 are swapped If it weighs (-2) 15, then eggs 8 & 10 are swapped Otherwise, it weighs 19 (+2) and the possibilites are 3&5 or 4&6 are swapped Weigh 3 If it weighs 5, then eggs 3 & 5 are swapped Otherwise eggs 4 & 6 are swapped

If you are in France, irrespective of the year, this looks like August when almost everybody is on 3 or more weeks vacation!