Europe and the United States got a look at each other's possible Ryder Cup pairings during practice on Tuesday.
Woods and Clarke hugged in a poignant moment at the K Club
Captain Ian Woosnam raised eyebrows by deciding to pair Spain's Jose Maria Olazabal and Sergio Garcia, with the duo not known as close friends.
Darren Clarke, playing with Lee Westwood, shared an emotional embrace with US star Tiger Woods.
Woods lost his father Earl to cancer in May, while Clarke's wife Heather died of cancer last month.
As expected, US captain Tom Lehman put Woods with Jim Furyk, David Toms with Chad Campbell, and Phil Mickelson alongside Chris DiMarco.
Wildcards Stewart Cink and Scott Verplank were paired with rookies JJ Henry and Brett Wetterich respectively.
Fellow debutants Zach Johnson and Vaughn Taylor made up the final pairing.
Lehman has already stated that he knows his pairings for the opening fourballs on Friday morning.
Several American players went out of their way to greet Clarke, with Woods embracing the Northern Irishman in a poignant reminder of the two players' difficult times away from the course.
Clarke received a warm reception from the crowd and spent several minutes signing autographs before starting his round with Westwood.
EUROPE PRACTICE PAIRINGS:
Group 1: Colin Montgomerie and David Howell, Paul Casey and Luke Donald
Group 2: Robert Karlsson and Henrik Stenson, Jose Maria Olazabal and Sergio Garcia
Group 3: Padraig Harrington and Paul McGinley, Darren Clarke and Lee Westwood
Europe captain Woosnam chose to keep nationalities together as far as he could.
In addition to Spain's Olazabal and Garcia, Ireland's Padraig Harrington and Paul McGinley were a pairing, as were Swedish rookies Robert Karlsson and Henrik Stenson.
And the in-form Paul Casey teamed up with world number nine and fellow Englishman Luke Donald, while Colin Montgomerie played alongside David Howell.
Casey and Donald have an impressive record as a pairing, winning the World Cup and, as amateurs, the Walker Cup together.
Scotland's Montgomerie was in the mood to entertain the already healthy crowds as Europe got their practice under way.
USA PRACTICE PAIRINGS:
Group 1: Tiger Woods and Jim Furyk, Scott Verplank and Brett Wetterich
Group 2: Chris DiMarco and Phil Mickelson, David Toms and Chad Campbell
Group 3: Vaughn Taylor and Zach Johnson, Stewart Cink and JJ Henry
Montgomerie sank a 20-foot putt, and quipped "it gets better than that" before walking across the green to hole from 30 feet.
"This is probably the strongest team we've ever had - 12 great players - and it's up to me to me only to get them pairings right," said Woosnam.
"I've put some pairings up for fourballs, then foursomes for Wednesday, but I'm going to have a look at how everybody is playing and talk to the lads.
"It's important to see how things go. There's so many pairings I can use."