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Can you explain why you think it has two correct interpretations? I obviously thought 15 min when I first read it and my brain didn't want to accept any other
by hmottestad 14y ago
Can you explain why you think it has two correct interpretations?
I obviously thought 15 min when I first read it and my brain didn't want to accept any other solution until I read the post below where it said 20 min and explained it as 2 pieces = 1 cut = 10 min, 3 pieces = 2 cuts = 20 min.
And now I can't see why my first thought was correct. Did you come up with some good rationale as to why it should be 15 min or other?
- redblacktree 14y agoIf you were to cut off two pieces of the board from an unknown source, you'd require two cuts. Three pieces would require three cuts (with the rest remaining behind). I don't think the wording really allows for this interpretation, but that is the only way I could explain the alternative answer.
- deleted 14y ago[deleted]
- SilasX 14y ago>Can you explain why you think it has two correct interpretations? Because it depends on whether you 1) require that the N pieces be congruent and 2) what counts as a cut. I think the textbook answer is based on assuming 1) no, and 2) cutting along a line segment at least as long as a side. Alternately, what counts as a "board" and a "cut". Then you get the answer by assuming you cut a square board in half, then one of the pieces into squares (which requires cutting along a line segment half as long).
- yew 14y agoSome people are arguing about whether 'cut into two' might really mean 'cut two off'. So I think your answer makes three interpretations (and nicely demonstrates that you do indeed have to specify things like "cutting is abstract and all cuts are of the same length"). The problem does specify 'works as fast' without any regard for length, though. And it obviously isn't actually a geometry problem because it doesn't even specify any ratios or angles - you could just cut a corner off and be done in a few seconds!
- hmottestad 14y agoLike that: ------------- | | | | | | |-----------| | | | | -------------
- hmottestad 14y agoOr you could say 11 minutes and do this: ------------- |/ | | | |-----------| | | | | ------------- Cut into two equal pieces and then cut off the corner :)
- josephg 14y agoThere's a picture next to the question of a saw cutting a straight thin plank. Its very unlikely that this interpretation of the question was intended.
- wampey 14y agoI agree with you here. If a board is 2 x 2 and you cut it in half, you have 2 1x2 pieces. That took 10 minutes. If you cut one of those 1x2 pieces in half you could have 2 1x1 pieces of board, and one 1x2 piece of board, thus 3 pieces. The first cut took 10 minutes, the 2nd cut, being half the size of the original took 5 minutes, thus 15 minutes.
- RivieraKid 14y agoPerhaps it's a really long stick and we are cutting off small pieces. Cut off one small piece: 1 cut. Cut of 2 small pieces: 2 cuts. Etc.