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The top nine at Solvemall Classic (Posted on 2010-06-01) Difficulty: 4 of 5
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?

See The Solution Submitted by broll    
Rating: 4.0000 (1 votes)

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Solution Solution(s) | Comment 10 of 11 |
I am assuming in all this that no two holes have the same distance.

The only shot distances that allow for the four definite holes and three/four of the uncertain holes are (assuming drives are longer than approaches, but it doesn't really matter):
drive: 130
approach: 20/110

With 110, distances 180 and 300 don't work. To get a unique answer for the total number of shots, they can be replaced by either 330 and 390, or 170 and 310.

With 20, the distance 180 doesn't work. To get a unique answer it must be replaced by 260.

Any of these three sets of distances gives a unique solution:
(150 170 200 280 310 350 370 410 500)
(150 200 280 330 350 370 390 410 500)
(150 200 260 280 300 350 370 410 500)


  Posted by snark on 2010-06-15 04:38:45
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