A pro golfer has the amazing ability to consistently putt distances of 3, 5, 7, and 11 feet. Strangely enough, though, those are the only distances he can putt.

Currently, our golfer stands on the green with his ball 20 feet from the hole. What's the fewest number of strokes he can use to get the ball into the hole?

Assume that if the ball is hit farther than the distance remaining to the hole, it will roll over to the other side without going into the cup.

  • $\begingroup$ Does he putt in the specific order of 3-5-7-11? Or can he for example putt 11 twice in a row? $\endgroup$
    – PirateSoul
    Jun 12, 2015 at 7:35
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    $\begingroup$ If he's good at measuring angles and he can putt 11 twice in a row, he can do it in two attempts. $\endgroup$
    – dmg
    Jun 12, 2015 at 7:37
  • $\begingroup$ @PirateSoul There is no specific order $\endgroup$
    – Wouter
    Jun 12, 2015 at 7:37
  • $\begingroup$ @dmg if you're sure that's the answer than put it as an answer :) $\endgroup$
    – Wouter
    Jun 12, 2015 at 7:38
  • 1
    $\begingroup$ @PirateSoul then go for it, 9.16515138991168 feet to the left or right :D Or, 24.61997733 degrees. $\endgroup$
    – dmg
    Jun 12, 2015 at 7:44

5 Answers 5


The answer is 2 shots. Granted the right angle, 2 circles with the radii of 11 will overlap as seen in the pic!

enter image description here

  • 4
    $\begingroup$ I don't see what's the point of drawing circles. what about just a triangle with sides 11,20,11? $\endgroup$ Jun 12, 2015 at 14:18
  • 9
    $\begingroup$ @user3453281: Drawing circles is the easiest way to find that triangle. $\endgroup$
    – Ry-
    Jun 12, 2015 at 17:32

Assuming that the golfer has to target the hole directly, i.e., no deviation by any angle, the answer is

4 strokes. Because all distances are odd, but the target distance is even, he needs an even number of strokes. Two strokes is impossible because no pair of distances adds up to 20. Using 4 strokes, however, there are multiple combinations: 7+3+7+3 or 5+5+5+5 or 7+3+5+5.

  • $\begingroup$ Or 11+3+3+3, 11+11+3-5, 11+11+5-7 $\endgroup$
    – aragaer
    Jun 13, 2015 at 8:56


He could take 0 strokes. Just pick up the ball and drop it in the hole.....and then run away yelling GOAAAAAAAAAL! (Any spectators would be so surprised and think he was crazy, that he just might get away with it)

  • 2
    $\begingroup$ @Luke He might have the potential of becoming the worlds best golfer.. $\endgroup$
    – Mark N
    Jun 12, 2015 at 13:48

According to the rules of golf, one stroke

Chip it in. A pro golfer that can only putt specific distances probably has better luck with his wedge. (A pro-level golfer should sink a ball on the green in one shot at least 35% of the time and in two shots at least 96% of the time. Our hero probably didn't make pro by 2-putting nearly every hole.)

Under the rules of golf, any club may be used for any stroke, even on the green

From USGA Rules FAQ:

Rule 14-1
Using Club other than Putter on Putting Green?

Q. Is it permissible to use a club other than a putter to play a stroke on the putting green?

A. Yes, the Rules of Golf do not stipulate the type of club that must be used for making a stroke on the putting green or anyplace else on the golf course.

  • $\begingroup$ But how do you know this will only take one stroke? There are no statements about how consistent his chipping skills are. $\endgroup$
    – Mark N
    Jun 18, 2015 at 19:03
  • $\begingroup$ @MarkN The other answers make a similar assumption that he will actually hit he ball at the correct angle and speed. The question asks for the theoretical minimum, not the expected average. Chipping on the green is rare at the pro level, but not as rare as only being able to hit 11-foot putts! As for feasibility, a pro sinking a 20-foot chip shot may not even make the highlight reel. $\endgroup$
    – Anon
    Jun 19, 2015 at 15:25

I'd say

two 11 feet putts, for he'll just have to put at an slight horizontal angle of approx 25°. He is not obligated to make a bee line, is he?


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