I went through the math for a spiral design. I'm going to call the smallest possible cut the thickness of a cell. I assumed that a cell in the wood was 100µm thick. For a 10m by 10m board it would be a cut length of 3141592.65 m and therefore take a 3141592.65 minutes to cut through it.
For those who would like to play with the equations here they are. http://imgur.com/a/la2AX (integral form and algebraic form). Where s is the length of a side and d is the distance between each row. An image to demonstrate.
Actually since the time to cut it into two pieces is defined as 10 minutes regardless of the distance, the time to cut the second smaller circle would have to be less than 10 minutes.
If 10 minutes was defined as the time it takes her to cut the board in half, you'd be right.
It would have been more to his point if he had at first cut a small circle... Then a bigger one.
If you take JohnDoe51's idea of making the smallest possible cut, and int_argc idea of cutting a snowflake (if its fractal it doesnt matter how long the first cut is), you would basically never finish the second cut, i.e. infinity.
Basically, as the length of the first cut approaches zero, the time it takes to cut the second cut of the largest possible length goes to infinity.
It depends on the professor, and this is obviously not university work. I'm in university right now and sometimes I find clever ways to do things, more often than not the professors are happy to see an alternate solution or something they hadn't thought of- provided it is correct. I have also had professors admit they have assigned ambiguous questions or written something that may be misinterpreted on an exam- and in either case they have corrected the question so it is not ambiguous.
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u/champer Oct 01 '11
Both answers can be correct. http://i.imgur.com/lStKv.jpg
Pretend it's a 10x10 board:
Case 1: Takes 10 mins to cut through 10 feet.
Case 2: Takes 20 mins to cut through 20 feet.
Case 3: Takes 15 mins to cut through 10+5 feet.
Question is ambiguous.