Damn, there is a bigger problem:

myjinxin katas #003 : Crossword puzzle

=> your kata is actually an almost perfect duplicate (there are some tiny differences, but nothing to make it different enough and this one has already rules for several solutions and surely have random tests already (I don't do JS so I cannot check for that, tho)). So it would actually be better that you unpublish yours, then solve the other and do its java translation... Damn, too bad...

error in the new solution setup: solvePuzzle() has to be non static, now. ;)

EDIT: and opening curly bracket missing for the constructor.

reopening to keep track of what's needed:

• you don't talk about mutliple solutions. Are they always unique? Especially, for the first example test, what if I return a grid with all words reversed? => You need either to give more information in the description or change the way you check the answer of the user (meaning: if it's not already done, I didn't try the kata yet. But the sample tests don't do that).
• missing random tests
• the suggestion of using instances rather than static method still stand, but there it's up to you (tho, I strongly recommand it, because that will make a better kata ;) )