ARTCC RADAR CTLR TURNED MLG AND OPPOSITE DIRECTION TRAFFIC; AT SAME ALT; TO PREVENT FURTHER LOSS OF SEPARATION. SYSTEM ERROR AND FLT CREW DEVIATION.

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RPTED IN AT FREQ CHANGE TO ZDC CENTER (134.2) AT 28.8 FOR 290. SHORTLY THE CTLR ASKED US OUT ALT (10 SEC) WE RPTED 290. WE WERE GIVEN A TURN 'IMMEDIATELY' LEFT ABOUT 90 DEG FROM OUR PRESENT COURSE AND ISSUED SIMILAR INSTRUCTIONS TO ANOTHER ACFT. DURING COMPLIANCE OTHER ACFT WAS SIGHTED AT 2-3 MILES DISTANCE (GREEN). WHAT WE HAVE HERE IS 2 ACFT AT SAME ALT; SAME JET WAY; DIFFERENT DIRECTIONS. CENTER STATED HE THOUGHT WE WERE SUPPOSED TO BE AT 280. WE ARE PRETTY SURE OF 290 ASSIGNMENT AS IT WAS READ BACK AND SET IN THE ALT SET AND WE HAD EXPERIENCED NO COM PROBS PREVIOUSLY. IT WOULD HAVE BEEN VERY INTERESTING HAD THE CTLR NOT GIVEN BOTH OF US HDG CHANGES WHEN HE DID. SOMEBODY SCREWED UP. CENTER RE-ROUTED US FROM OUR FILED (NORMAL CLRNC) OF LGA WHITE; MXE;J75GSO;J14SPA;GSO TO LGA WHITE; J209 COYLE J37GVE; J75GSO; J14SPA DIRECT GREER (GSP). MANY SPD CHANGES; SOME CONFUSION ON DESIRED SPD FROM CTLR; TO CTLR. I.E. ONE SAYS RESUME 300 NEXT ONE SAYS SLOW 280; THEY NEEDED 20 IN TRAIL THEY SAID PREVIOUSLY GIVEN TWO TERMS FOR SPACING. SUPPLEMENTAL INFO FROM ACN 90017. MY F/O SAID HE SAW A SMALL ACFT IN A TURN AT APPROX 2-3 MILES. WE INQUIRED WITH THE CENTER ABOUT WHAT HAD HAPPENED. HE STATED HE THOUGHT WE WERE CLRED TO 28;000 ALSO GAVE US A DSCNT TO 28;000' THAT TIME. WE RESPONDED OUT OF 29;000' FOR 28;000. WE TOLD THE CENTER IT WAS OUR UNDERSTANDING WE HAD BEEN CLRED TO 29;000 AND HAD TO THE BEST OF OUR KNOWLEDGE PREVIOUSLY RESPONDED TO CLB TO 29;000 AS IT WAS SET IN OUR ALT SET.