= Solution
A physical <baryon> is a <colour singlet>. Its three-quark colour factor is antisymmetric, proportional to $\epsilon_{abc}|abc\rangle$. In the hypothetical scalar-quark theory, the <quarks> obey <Bose-Einstein statistics>, so the complete three-particle state must be symmetric under exchange. At $L=0$ the spatial factor is symmetric, and three zero spins supply no nontrivial <spin> factor. The flavour factor must therefore be antisymmetric to cancel the antisymmetry of the colour factor.
There is exactly one completely antisymmetric state made from three flavour basis states: the <flavour singlet of three scalar quarks>,
$$
|F\rangle=\frac1{\sqrt6}\bigl(|uds\rangle+|dsu\rangle+|sud\rangle
-|usd\rangle-|dus\rangle-|sdu\rangle\bigr).
$$
Equivalently, $\dim\bigwedge^3\mathbb C^3=1$. A repeated flavour gives zero under complete antisymmetrization. \b[Only one ground-state flavour singlet, containing $uds$ and having $J^P=0^+$, remains.] Keeping fermionic exchange antisymmetry while changing the spins to zero would contradict the assumed <Spin-statistics theorem>. The standard antisymmetric colour factor and the ordinary-quark flavour decomposition are documented in the quark-model review.<Review of Particle Physics by Particle Data Group (2022)>[<Quark> Model, §15.5, equations (15.22)–(15.24)]{ref}
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