Endarkenment

Hail and well met Sir R-----! As you can see, reports of my demise have been greatly exaggerated! No, I have spent these last several months in Persia at the express invite of the Caliphate. As you are no doubt aware Musulmen have a peculiar fascination with matters astronomical and, what with my being something of a favourite in the heavenly courts, their acamedicians were keen to record for posterity my testimony regarding the customs and culture of their subjects.

But here you are dry! Come, take a seat and a draught of this very fine brandy. May I take it that you are no less a sportsman today than when last we met?

Splendid! Then let us fortify our refreshment with a wager!

I have in mind a game most popular in Persia. It was invented by one of their academicians, Al something-or-other as I recall. It seemed that most everyone I met in Persia was called Al; how they could discern from whom the salt was to be passed escapes me entirely!
This particular Al was apparently a mathematically minded fellow who wrote games and puzzles for light relief from his work, although one wonders what relief could possibly be required from adding up numbers for a living. Methinks these academical fellows should try their hands at soldiering should they wish to learn the true meaning of hardship; remembering to carry your ones and twos and threes and such seems to me no great matter compared to facing down an army of moon-men armed with nothing but a darning needle and a pocket handkerchief!

But I digress.

Now this Al fellow explained the rules of his game to some several fellows of his who then did the same and so on and so forth and suchlike until it had become a well favoured passtime in those parts.
Here, I shall lay out some ten by ten tiles representing lit and unlit lamps as takes my fancy. You may take turns turning over four tiles at a time, from lit to unlit or contrariwise, with the constraint that each must neighbour another, either horizontally or vertically, with the topmost row considered a neighbour to the bottommost and the leftmost column a neighbour to the rightmost.
If you can contrive to make all of the tiles unlit you may have a coin from my purse; if not, I shall have one from yours.
If a single coin strikes you as a meagre prize, I have another proposal; I shall set a limit of fifteen turns and for every turn less that you take to endarken the board I shall give you one coin of mine and for every one more you shall give me one of yours.

I once described the rules of this game to that malodorous student with whose acquaintance you will recall I am most cruelly burdened. Needless to say he had naught remotely relevant to remark, but rather started wittering on incoherently about satisfactorily exercised bulls and parrots! Quite why he imagines I'd have even the vaguest interest in the fitness of his menagerie I cannot begin to fathom.

But let us not sully our evening with talk of that wretched cur; take another draught and think upon which wager, if either, you might take!