The problem with Races

Number Theory Level 5

Suppose that there are only 2 races of humans, Race A and Race B, and that an offspring acquires an exact $50:50$ split of races from his parents.

Is it possible for any one person right now to be exactly $\frac{1}{3}$ of Race $A$ , and $\frac{2}{3}$ of Race $B$ ? Assume no instances of pedigree collapse, i.e., incestuous procreation, inbreeding, etc.

No, it is plainly impossible even for an infinite number of ancestors. Yes, even if there are a finite number of ancestors No, because there needs to be at least

3

originating races for someone to reach that point. Yes, if his number of ancestors are made as large as possible

1 solution

Efren Medallo
Jun 14, 2017

At the ideal circumstances stated above, a person shall have $2^n$ ancestors for the $n^{th}$ generation before him. Since the number of his ancestors will always be powers of $2$ , there can never be a case where exactly $\frac{1}{3}$ of them are from Race $A$ , and the remaining from Race $B$ . This is also true regardless of the number of races present in a generation.

The problem with Races

1 solution

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