Hearted Youtube comments on Mathologer (@Mathologer) channel.
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15:23, I arrived at the same answer as the Talmud, by the following reasoning: the contested child ("red") who has a possible claim to the 1st son's estate takes first pick, and is given half-way between what he would receive in the two scenarios: (1/2 + 1/3) / 2 = 5/12. What remains (7/12) is given to his two siblings, and is shared equally between them, so they each take 7/24.
My reason for giving the "red" child precedence was more of a practical than a legal one: it's messy to modify the fractions for all the children at once, and you can easily end up with something that doesn't add up to 1. By first settling the "red" child's claim, it's then trivial to divide what remains between the "green" children.
Interestingly, we can go about it the other way, settling the "green" claim first: (1/2 + 2/3) / 2 = 7/12, then 5/12 remain for the "red" child. So, the solution is the same regardless of who takes first pick, which is definitely a plus.
A more modern approach would be to assign the two scenarios some probability, then divide between them in proportion to how likely they are; but given that no information is available about the paternity of the "red" child, a 50-50 divide is kind of forced.
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