1. No penalty. The Local Rule states that a ball may be marked, lifted, cleaned and placed, not must.
2. No penalty. The ball may be placed anywhere that is within one club length, provided it is not in a hazard and not on a putting green.
3. One stroke penalty. The Local Rule states that the ball must only be placed once and is in play when it has been placed, so the player is penalised for touching their ball in play, Rule 18-2.
4. Two strokes penalty. The Local Rule requires that the ball is placed and not dropped, Decision 20-6/1. However, if the player realises that they should have placed the ball before making a stroke at it, they may still lift the dropped ball and place it within the permitted area without penalty, Rule 20-6.
5. Two strokes penalty. Rule 25-2 only provides relief for a ball that is embedded in a closely mown area and so there is no relief for the embedded ball under this Rule or the Local Rule. The ball should not have been lifted and dropped and was therefore played from a wrong place, Rules 18-2 and 20-7.
6. One stroke penalty. The accidental movement of their club-head, which was being used as their ball-marker, was not in the specific act of marking the position of the ball. Rule 20-1. This illustrates one good reason why players should never use this method of marking their ball anywhere on the course
7. Two strokes penalty (in addition to the penalty for taking relief for an unplayable ball). Players must always drop their ball according to the Rules (e.g. ball deemed unplayable, relief from a path, relief from casual water) before placing it under this Local Rule. The logical reason is that the player does not know where to place their ball before the drop is made. For example, in this question the ball may have been dropped within two club-lengths of where it was deemed unplayable and could then have rolled back close to where it originally lay, which would then be the reference point for placing within the permitted area. Having dropped the ball under penalty of one stroke, the player may then mark, lift, clean and place their ball under the Local Rule.
8. Two strokes penalty. After being placed the first time the ball was at rest and therefore back in play as soon as the player took their hand away from it. Because they did not cause the ball to move it should have been played from where it came to rest after falling off the tuft. The Local Rule states that the ball must only be placed once and is in play when it has been placed.
9. One penalty stroke. The Local Rule specifies that the ball must be placed, not rolled with a club.
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