I disagree with your logic. As the corner-cut solution shows, there are only two sane answers. "20 minutes" where you have cuts across the plank or "any* amount of time whatsoever" where you allow any kind of cut.

There is no sufficiently logical way to get to any particular number other than 20; the shape of the plank does not allow you to cut across and make your cuts intersect like you might with a square board. There is no reason on this particular shape to prefer "15 minutes" over "14 minutes" or "25 minutes". It all gets lumped into "any amount of time whatsoever".

If "any amount of time whatsoever" was an acceptable answer it wouldn't make sense that a single cut takes 10 minutes, so we should discard that answer. This leaves only one candidate answer, 20 minutes.

*"any" would be limited by how long of a diagonal you can make but it would be hours

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?

If 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.

>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).

Some 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!

I 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.

Lumber has three dimensions.

I read 2x2 and thought,"that's not a board!" and wondered why s/he was cutting it lengthwise to get 1x2.

If it was dressed, that 1 might be very small indeed.

Like that:

  -------------
  |     |     |
  |     |     |
  |-----------|
  |           |
  |           |
  -------------

Or you could say 11 minutes and do this:

  -------------
  |/          |
  |           |
  |-----------|
  |           |
  |           |
  -------------

Cut into two equal pieces and then cut off the corner :)

There'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.

Perhaps 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.

>but the question allows different interpretations and both answers are correct assuming different interpretations.

There is only one logical interpretation (though you'd have to actually think past the conclusion your brain jumps to), the question was perfectly clear about the board being cut into two pieces.

> The correct answer would be "I do not know, this problem is under-specified."

In that case, I'd write my assumptions about the problem and show how I arrived at the solution. If the teacher still says it's wrong, I probably won't bother arguing - I don't waste my time arguing with morons.