Due　to　the　nonlinear　nature　of　contacts,　the　real　contact　information　is　indeterminate　and　there　is　no　analytical　solution　for　discontinuous　computation.　In　the　context　of　two-dimensional　discontinuous　deformation　analysis　(2D　DDA)　for　arbitrary　polygon　block　systems,　the　contact　indeterminacy　arises　from　at　least　two　aspects,　namely　kinematics　and　geometry.　This　study　provides　a　specific　numerical　solution　for　2D　DDA　to　address　the　indeterminacy　problem　of　contacts　between　arbitrary　polygon　blocks.　First,　local　contact　boundary　is　established　by　defining　the　solid　angle　of　2D　blocks　and　the　entrance　solid　angle　between　two　2D　solid　angles　of　two　blocks.　Second,　the　linearized　first　entrance　formulas　are　derived　to　estimate　the　first　entrance　time　and　position.　Third,　an　enhanced　shortest　exit　strategy　based　on　entrance　angles　is　introduced　to　provide　a　unified　solution　of　the　contact　points　and　direction　of　closed　contacts.　Some　extreme　and　challenging　examples,　including　oblique　collision　contacts,　undue　penetration　contacts,　genuine　vertex-vertex　contacts　(including　absolutely　symmetric　contacts),　extremely　abnormal　block　contacts　(i.e.,　contacts　between　extremely　short　edges　and/or　sharp　angles),　multi-connected　block　contacts　and　numerous　singular　contacts,　demonstrate　the　accuracy,　robustness　and　application　prospects　of　the　proposed　method　in　addressing　difficult　contact　problems.