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?