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I wonder if surface like this could thwart a 1-putt, with an appropriate velocity limit $v_0 \le v_{\max}$?
         Two Bumps http://people.csail.mit.edu/%7Eorourke/MathOverflow/GreenTwoBumps.jpg
The cup $c$ is directly ahead of the ball at $b$, directly along the line indicated by the arrow. Clearly putting straight or left of that arrow sends the ball off to the left. It seems that reasonable velocity conditions might ensure that angles $\epsilon$ right of the arrow would still roll left of $c$ from the influence of the left slope of the second knoll, and that aiming further rightward would roll off the right slope of that second knoll.