▁if ▁all ▁queries ▁answered ▁so ▁far ▁were ▁outside ▁the ▁ ε - ne igh bour hood ▁of ▁x ▁and ▁y , ▁then ▁agent ▁i ▁has ▁no ▁way ▁to ▁know ▁whether ▁we ▁are ▁in ▁the ▁old ▁R MS ▁or ▁in ▁the ▁new ▁R MS . ▁ ▁E qui pped ▁with ▁this ▁knowledge , ▁an ▁advers ary ▁can ▁trick ▁every ▁env y - free ▁division ▁protocol ▁to ▁go ▁on ▁forever : ▁ ▁Start ▁with ▁any ▁R MS , ▁e . g . ▁with ▁parameters ▁x   =   1 / 3 , ▁y   =   2 / 3 , ▁s   =   0 . 3 ▁and ▁t   =   0 . 3 5 . ▁ ▁As ▁long ▁as ▁the ▁protocol ▁makes ▁cut s ▁at ▁points ▁other ▁than ▁x ▁and ▁y , ▁let ▁it ▁continue . ▁ ▁When ever ▁the ▁protocol ▁asks ▁agent ▁i ▁to ▁make ▁a ▁cut ▁at ▁x ▁or ▁y , ▁switch ▁to ▁a ▁different ▁R MS ▁with ▁x ' ≠ x ▁and ▁y ' ≠ y , ▁making ▁sure ▁that ▁the ▁values ▁are ▁the ▁same ▁for ▁all ▁previously ▁made ▁cut s . ▁Thus ▁the ▁protocol ▁can ▁never ▁make ▁cut s ▁at ▁the ▁correct ▁x ▁and ▁y ▁required ▁for ▁an ▁env y - free ▁division . ▁ ▁Appro xim ations ▁▁ ▁Since ▁env y - free ▁c ake - cut ting ▁with ▁connected ▁pieces ▁cannot ▁be ▁done ▁in ▁finite ▁time , ▁c ake - cut ters ▁have ▁tried ▁to ▁find ▁work - ar ounds . ▁ ▁One ▁work - around ▁is