Posted 13 August 2007 - 07:56 AM

Maybe I'm just not understanding the solution, but I don't think that everything is clear enough.

First of all, I agree with manisdogfish. Maybe we don't understand what devalue means in this sense.

Then, assuming that touching the lentils does not devalue, I have a problem with volume. The way I picture this, we get an hourglass shape. So, we fill the innkeepers bag halfway, then tie it up, and turn it inside out. However, since its bound halfway, the empty top half if really going to be fitting around the bottom half. So, if we do actually fill it up halfway, then the top half will now also be full. Thus, no more room for the peas.

I realize that I have assumed that the peas and lentils fill up the bag, half and half. However, the problem never specified. I think it should. The farmers bag could be filled up, but its the size of the innkeepers bag that matters (in relation to the amount brought it). If the lentils fill up one-third of the bag, then its turned inside out, the remaining two-thirds will now be half filled by the bound-up lentils. If the peas also amount to one-third of the innkeepers bag, then there is enough room in the inverted top half.

If I look at it more, even one-third is too much in some respects. It would have to one-bound-up-third. One-third of a non-bound-up bag is obviously more than one of three bound-up sections. This has to do with surface area of the actual sack.

Forgive me if I've ranted. I kind of hope someone shows me a something I didn't think of to make this solution a little more valid. I have found myself proven wrong several times when I do not agree with a solution. Its always before I go so far as to post about it, though. If anyone agrees with me, then I just think the problem should be re-phrased. I do appreciate the solution, but I believe the problem was an after-thought of the solution.