Cink praised the crowd at St Andrews after bowing out with a two-over 74 to finish one over par.
The South African carded a one over par 73 to be joint 81st, with Swede Pierre Fulke heading the field by one shot after powering to a six-under 66.
Clarke and Bjorn both picked up two shots early on but their challenge faded with some wayward play and they had to settle for one over par 72s and a share of fifth place.
Montgomerie was suddenly one over par and seven adrift of Siem and Australian Andrew Dodt at that stage before dropping from 14th to 47th by taking a shocking 42 to the turn and handing in a 76.
The Chinese schoolboy not only set the record as the youngest player to ever compete at the Masters, he then followed that up with a round of one-over par.
The Northern Irishman clawed back a couple of shots, and nearly holed his approach to the 18th, but at one-over par for the tournament is too far back to mount a challenge.
The 27-year-old is perfectly poised, three shots behind the leader, despite a disappointing one-over-par 72 on day two.
Kathryn Marshall and fellow Scot Catriona Matthew were the best-placed British competitors on one-over-par 289, 16 shots behind Webb.
Vidoes rolled and mobile phone cameras clicked as Nicklaus and Couples went round in a one-over-par 73 to 'win'.
Saturday saw him card a disappointing one-over-par 73 to leave him 12 shots behind runaway leader Louis Oosthuizen and with only pride to play for.
World number one Luke Donald of England failed to capitalize as he struggled to a two-over par 74, one better than compatriot Lee Westwood who finished with a disappointing 75.
Anything par or one over is going to be flying up the leaderboard.
His playing partner, Spain's Sergio Garcia also had a disappointing day posting a three-over par 75 to leave him one-under after three rounds.
But Ireland's Padraig Harrington, who shared the overnight top spot with Rose, dropped back to five under par after hitting a one-over round of 71.
The world No.12 carded a torrid seven-over-par 79 on day one at the Muirfield Village Golf Club, his highest score in 43 rounds at the venue.
Masters champion Mike Weir lies second on level par, with Open champion Ben Curtis one over and USPGA winner Shaun Micheel two strokes back.
Garcia, who started with a one-shot lead over Woods, was in the fairway on the par-5 second hole.
The 42-year-old American opened with a disappointing one-over 73 but has charged through the field by playing the next two rounds in 15-under-par.
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