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We make a compelling case that FQHE is possible here for fully spin polarized composite fermions, but with an unconventional underlying physics. Thanks to a rather unusual interaction between composite fermions, FQHE here results from the suppression of pairs with relative angular momentum {\\em three} rather than one, confirming the exotic mechanism proposed by W\\'ojs, Yi and Quinn [Phys. Rev. B {\\bf 69}, 205322 (2004)]. 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