jfgw wrote:While not stated in the question, a practical restriction would be that the boards are probably tongued and grooved. This would allow the last row to be cut length-ways but would not allow, for example, three boards of width 6cm to be cut from one board and placed side-by-side (or one each side of the floor) to make up the odd 12cm. ...
Agreed, but there are plenty of other practical issues that affect a real-world solution - e.g. the questions you raise about positioning with respect to joists and about whether the ends are also tongued and grooved (which doesn't just affect where cut ends must go, but also which wall they must be against and hence when a piece has been trimmed both lengthwise and widthwise, which corner it must go into), the fact that in real life, a saw cut has a nonzero width and so wastes a small amount of material, and the difficulty of sawing a very small amount off the end of a plank (obviously that doesn't affect the cuts that take off pieces you're going to use, but it could affect taking off small pieces of scrap).
So basically, one can either treat the question as a puzzle, or as a practical issue that requires quite a few extra details to be given before it can really be answered. Given the title of this board and the fact that the question supplied enough detail for a puzzle but not enough for a practical issue, I basically chose the former interpretation, only noting practical issues when ignoring them led to truly silly 'solutions' such as the slice-into-50-paper-thin-layers one.
By the way, that's not saying that I think the board's title forbids practical questions, just that if a question doesn't say clearly that it is a practical issue and it could be taken either as a puzzle or as a practical issue, the default is to treat it as a puzzle. I.e. if one wants a question to be treated as a practical issue,
say that it is one! Though it might actually be better to post it to an appropriate other board, such as the Building and DIY one in this case, to get a better chance that the practical details will be addressed properly, with a crosspost here when an issue has strongly puzzle-like aspects. And having thought to look for such a board for the purpose of this post, I note that JMN2 has in fact recently
posted about flooring there. It isn't totally clear to me whether this is about the same flooring job, but the 19.2cm width of the boards does look to be a common feature...
jfgw wrote:... The OP does state the following, however, which applies the same restriction:
JMN2 wrote:The planks are 19.2cm wide so the width takes 16 rows of planks of which one is cut to roughly half lengthwise.
That's not a restriction, at least as I read it - it's just an observation about what fits the room's width. It would need to read as something like "The solution is to use 16 rows of 19.2cm-wide planks of which one is to be cut to roughly half lengthwise" to be a restriction.
Gengulphus