My pal is very fond of puzzles, but can't always remember all the details correctly. Yesterday he told me about a new version of the famous 9-hole golf problem.

‘OK, there’s this guy, and when he plays golf, he always uses one of 2 shots. He always aims straight for the hole; if he overshoots, then he plays back towards the hole with his next stroke…'
‘Yes, I get the idea. You’re saying that he has a drive of, say, x yards, and an approach shot of, say, y yards, some exact combination of x's and y's will always enable him to sink the ball. What are the lengths of the holes?’
‘Gosh, that’s the problem! I can only remember 4 for certain; 150 – that was the shortest - 200, 350, and the longest one was 500.’
‘And what do you ‘remember’ the rest were, old buddy?’
‘Hmmm, something like 180, 280, 300, 370, and 410 - but now I come to think about those numbers, I’m pretty certain that one or two of them are wrong.’
‘And how many strokes altogether?’
‘Hehe, that was what you had to work out – but none of the holes was less than 150 yards, and none took more than 5 shots.’

Can anyone tell me what the correct lengths of the 9 holes were, so that I can work out the original problem?

(In reply to re: computer by broll)

What's wrong with the following as the original puzzle about which your pal is talking?

The holes on the course have lengths 150, 200, 280, 300, 320, 350, 370, 410, and 500. What's the total number of strokes for the golfer who has only two distances to send the ball?

150: 130 + 20:             2 strokes
200: 2*130 then 3*20 back: 5 strokes
280: 2*130 + 20:           3 strokes
300: 2*130 + 2*20:         4 strokes
320: 2*130 + 3*20:         5 strokes
350: 3*130 then 2*20 back: 5 strokes
370: 3*130 then 20 back:   4 strokes
410: 3*130 + 20:           4 strokes
500: 4*130 then 20 back:   5 strokes
                      ---------------
                total:    37 strokes
                

But substitute a 240 for the 320, and you get two strokes less, as the 240 is accomplished with 2*130 then 20 back.

In either case, the original puzzle would have been solvable, with the answer 37 strokes in the one case, or 35 strokes in the other. And there are the other possibilities mentioned in my first comment.

Posted by Charlie on 2010-06-02 03:32:19