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And that chance still existed as he made the turn, even coming off consecutive birdies, which put him on the cut line with nine holes to play.
But Woods typically doesn't worry about such things. Or at least he doesn't admit it.
A low score was on his mind so that he could get back into contention, not make the cut.
He didn't quite accomplish his goal, but at least he's around for the weekend at a TPC Sawgrass course that has been nothing short of maddening for him through the years.
Woods shot a 4-under-par 68 -- just his fourth score in the 60s at the course in his past 21 rounds -- to move from a tie for 100th entering the second round into a tie for 30th heading into the weekend.
"I was trying to shoot my number today, and I thought that would put me four or five back ... 66 was my number," he said. "I figured that would have been a good way to go back into the weekend. It would have put me four back. But I'm still with a good chance."
Woods finished at 2-under 142, and the cut came at 144, with 72 players advancing to the weekend. He trails tournament leaders Zach Johnson, Kevin Na and Matt Kuchar by six strokes.
The 68 was his first in the 60s here after nine straight at 70 or worse. Since winning the tournament in 2001, Woods barely has been a factor, posting just one top-10 finish -- eighth -- in 2009. The past two years he has withdrawn with injuries.
But Woods got some momentum with four straight birdies Friday at the eighth, ninth, 10th and 11th holes. He birdied three of the four par 5s as well, a sore spot in his recent struggles at the Masters and the Wells Fargo Championship, where he missed just the eighth cut of his pro career. Woods had put himself in position for consecutive missed cuts with an opening 74 here.
The cut claimed No. 1-ranked Rory McIlroy, No. 5 Hunter Mahan, No. 6 Steve Stricker -- whose consecutive cut streak ended at 49 on the PGA Tour -- and No. 9 Webb Simpson, who missed his first cut of the year.
Woods is among several players tied at 30th, including Phil Mickelson, who won here in 2007. And Woods improved nearly all aspects of his game. He hit 10-of-14 fairways, 14-of-18 greens and needed just 28 putts.
"It's a challenge, it's an absolute challenge," Woods said of the TPC course that never has seen a repeat winner and never seems to allow anyone a long run of success.
"It's one of those things where you just have to hit the ball well at the right time. You just have to hit the ball well all week. ... You just can't take it around this place.''
Woods will tee off well before the leaders at 11:25 a.m. Saturday with Keegan Bradley. Johnson and Na are in the final group at 2:35 p.m.