The solution is simply the throw-in at followed by making an eye at
. The result is, the group with an eye wins the capturing race since there is no way for White to make approach moves to Black's group.
If ataris, then
can make an approach ko. After taking the ko back White cannot win it right away, but must play atari in the corner to make it a regular ko.
Playing first is getting the order of moves wrong.
and
makes seki.
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