A ZDC ARTCC RADAR TRAINEE CTLR DSNDED A B737 TO AN ALT OCCUPIED BY HS25 ON A CONVERGING COURSE.

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TRAINEE HAD TAKEN HDOF ON ACR X OVER GVE VOR AT FL350. ACFT Y WAS NBOUND TO GVE AT FL330. TRAINEE DID NOT SEE THE ACFT Y; ALMOST HEAD-ON DUE TO MANY DATA BLOCKS IN THE AREA; AND DSNDED ACR X TO FL330. THERE WAS ANOTHER ACFT BELOW THE ACR X AT FL310 SO COULDN'T DSND HIM ANY FURTHER. I TRIED TO TURN THE ACFT BUT THEY DID NOT ANSWER! IF THE ACFT WOULD HAVE LISTENED TO THE FREQS THEY WOULD HAVE BEEN SEPARATED IN TIME. SUPPLEMENTAL INFO FROM ACN 637859: SLIGHT BUMPY AT FL350; ASKED FOR FL310; ADVISED NEXT CTLR WOULD HAVE DSCNT CLRNC CHANGED FREQS. SHORTLY THEREAFTER; CTLR GAVE US A CLRNC TO FL330. AS WE WERE DSNDING THROUGH FL34;. THE CTLR ASKED FOR OUR ALT. AS I RESPONDED 'FL346 FOR FL330;' I OBSERVED TCASII TFC AT 3 NM 10000 FT AND LEVEL AT FL330. I ASKED THE CTLR WHAT HE WANTED US TO DO. HE RESPONDED 'TURN R TO 270 DEGS.' I RESPONDED THAT WE WERE MAKING AN IMMEDIATE R TURN. AS WE COMPLETED THE TURN; THE CTLR CLRED US BACK ON COURSE. I SUBSEQUENTLY ASKED IF THERE WERE ANY SIMILAR CALL SIGNS ON THE FREQ. THE ANSWER WAS NO; BUT SHORTLY THEREAFTER I HEARD ACFT ON THE FREQ. HE WAS IN FRONT OF US AND HEADED FOR CLT ALSO. MY GUESS IS THAT I HEARD THE CLRNC FOR THE OTHER ACFT TO DSND AND THOUGHT HE WAS CALLING US. I'M ALSO SPECULATING THAT MY READBACK TO THE CTR WAS BLOCKED BY THE OTHER ACFT. ALL THE SPECULATION TURNED OUT TO BE INCORRECT; AS I CALLED ZDC AFTER GATE ARR. FROM THE RANKING SUPVR I LEARNED THAT WE HAD IN FACT RECEIVED THE DSCNT CLRNC BUT THAT IT HAD BEEN MADE IN ERROR. THE TAPES HAD ALREADY BEEN REVIEWED AND OUR CREW WAS CLRED OF ANY WRONG DOING. WHILE TCASII WAS A FACTOR IN ALLOWING US TO IMMEDIATELY IDENT THE ERROR; THERE WERE NO TCASII TA'S OR RA'S ISSUED.