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I'm not totally sure about "zigzag". Is it literally L?R, then down, then L/R etc?

If so, I have some problems:

I've got the two solutions for 31 ( as well as 30), so they must both go right, then down. One must eventually go through Square 42, but neither of them fit.

The solutions for 45,46 are suspiciously similar, but presumably aren't superimposed. Putting them in gives me trouble with 37 - help, please.

Dylan, from the clues I have solved, they fit going across and down but not necessarily one up one down each time. It could be two across cells then two down cells for example.

I am baffled by the meaning of the phrase 'zigzags either left or right and down'. I parse this as 'either left and down or right and down' (feeling that I need to use brackets!). This would result in an ordinary zigzag with directions at 45 degrees to the sides. But then the other reply suggests that the zigzag is oriented parallel to the sides, so some of the entries are across left or right and some are down.

I have answered quite a lot of the clues, but am finding all sorts of inconsistencies when I try to enter words.

When I first read the preamble, I thought it meant that entries changed direction after each letter. I now realise that this is not the case. My only concern is whether an entry can "zig" left after having "zagged" right earlier (and vice versa). The preamble implies that it can, otherwise it should have read "left and down or right and down". Plenty of clues solved and token starts made at entries in the top right and bottom left corners.

Further thought: could it mean

zigzags left: in other words, oscillating up and down toward the left
zigzags right: the same but rightwards
zigzags down: zigzags in a downward direction

It might be possible to fit in more of my solutions this way.

I find it very annoying that no subeditor has commented on the need to resolve an unnecessarily vague description.

Unless some kind soul can explain the precise meaning of the preamble then I fear that this one will be filed in the "Life's too short" bin.

I read 'zigzags left and down' as starting SW, then alternating with SE and similarly 'right' is SE/SW - which means a n-letter solution will go down into n rows, and the four empty cells would have to be the unnumbered ones in the top row. However this leaves no room to comply with the given number of cells used at 43 & 44 etc.

Can someone please give an unambiguous description of the allowable entry paths ?

I think now, having solved more clues, and particularly from the top right corner, that there are no diagonal moves. So the zigzag consists entirely of 'horizontal' moves (either left or right, but not a combination of both) together with down moves. I suppose that is the 'obvious' interpretation of 'either left or right and down' but I was thinking of diagonal moves as satisfying that description.

It would presumably be acceptable to have an entry going down or across only - a sort of null zigzag - but I think that is unlikely.

Having completed the top right hand corner of the grid, I am now pretty sure that the zigzags consists of horizontal (ie left or right segments, but not both) and down segments. Theoretically this would allow an entry which only went down (a sort of null zigzag) but I doubt that would happen.

Sorry, posted twice, because I thought the application had rejected the first one!