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Commander Steve Rogers has decided Wolverine is a threat to the country's best interests and wants him either captured or incapacitated. He is given the knowledge of Logan's whereabouts 24 hours from now, and immediately prepares to have him brought in. Logan, conversely, has 24 hours notice that Rogers is going to be bringing him down. Steve has access to any and all resources/personnel feasible for him to use given his position as the head of security for the nation.

How long does it take for Rogers to achieve his mission? What would it take for Rogers to either capture Logan, incapacitate him, or even kill him?

OR...

Does Logan manage to evade capture indefinitely or somehow wind up killing Rogers?

12 minutes. 11 minutes to find Wolverine. 1 minute for Steve to choke Wolverine out.

Commander of what? S.H.I.E.L.D.? H.A.M.M.E.R.?

Originally posted by Parmaniac
Commander of what? S.H.I.E.L.D.? H.A.M.M.E.R.?

They're both defunct. He's in charge of the country's security, which includes the Avengers.

Originally posted by Sr J-Bieb
12 minutes. 11 minutes to find Wolverine. 1 minute for Steve to choke Wolverine out. AMERICA!

Wolverine isn't big on running or preparation the first thing he does with his 24 hours of prep is track Cap down and put the boots to him while Steve is strategizing.

The op says Steve knows where wolverine is gonna be... It doesn't say wolverine knows where Steve is...

Steve drops a helicarrier on wolverine.
:-)

Wolverine checks Steve's twitter feed.

but that makes no sense, if wolverine gets notice that CA will come for him in 24 hours he'd change plans and go into hiding or prepare to take the fight to cap. Either way, his location would become unpredictable unless Cap's info comes from a precog which makes it impossible for logan to to evade in the first place.