JohnK said:
			
		
	
	
		
		
			I would be interested to find out how many teams have scored 6 dec 551 in the first innings and have lost the test match or put themselves in a position to lose a test match.
		
		
	 
The highest score by a team to not win or draw is Australia's 586 in 1894 (timeless test - lasted 6 days).  Scores Australia 586 all out, England 325 all out & 437 all out (follow on), Australia 166 all out - England win by 10 runs.
Next highest non-winning/drawn score is Pakistan 574/8d (batting 2nd) in 1972/73.  Scores Australia 441/5d, Pakistan 574/8d, Australia 425 all out, Pakistan 200 all out - Australia win by 92 runs.
Next is the tied game in which Australia made 574/7d in 1986.  Scores Australia 574/7d, India 397 all out, Australia 170/5d, India 347 all out.
Next is Australia 556 all out in 2003.  Scores Australi 556 all out, India 523 all out, Australia 196 all out, India 233/6 - India win by 4 wickets.
So 1 team has scored more in an innings, declared and lost.  Another scored more, declared and tied game.  2 others scored more, bowled out and lost.
As for how many have put themselves in losing position - no way to answer that.