The short answer: Yes.
It's counterintuitive, becase declaring a ball unplayable when, in fact, the ball is eminently playable seems counter to the basic golf principle of "play it as it lies."
In the scenario described above, the golfer would remove the ball from the bunker, assess himself a 1-stroke penalty, place the ball at the spot of the original putt and try again. You never, ever see pros doing something like this because pros are unwilling to take the penalty. A golfer who is terrified of sand (pros consider sand shots among the easier shots in golf) might, however, think that 1-stroke penalty is worth it to get out of the sand.
Fact is, a golfer can declare any ball unplayable, at any time, for any reason, and anywhere on the course other than in a water hazard. The penalty is one stroke with three options for how to proceed.
In the rulebook, it's Rule 28, Ball Unplayable, and it's as straightforward as can be:
"The player may declare his ball unplayable at any place on the course except when the ball is in a water hazard. The player is the sole judge as to whether his ball is unplayable."
After taking a 1-stroke penalty, the three options for proceeding are to return to the spot of the previous stroke and play again; or drop within two club lengths, not nearer the hole; or drop behind the spot, going back as far as you want, keeping the original spot between the hole and the new place where you drop.
If you declare a ball in a bunker unplayable and use the second or third option (taking a drop), you must drop in the bunker.
For a little more explanation, read Rule 28. It's every bit as clear as it sounds, even if that doesn't sound quite right.
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