On Fifteen Love

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In their most recent game, Sir R----- was challenged to pick cards from the ace to nine of hearts so as to play a trick of three cards that summed to fifteen, counting the ace as a one, taking turns so picking with the Baron. If Sir R----- were to manage to do so before the Baron and before the cards were exhausted, he should have had a prize of one coin, forfeiting one if he weren't.

The simplest way to figure whether Sir R----- should have taken on the Baron is to arrange the cards in a magic square.

     
     
     

As can be plainly seen, every row and column sum to fifteen, as do the diagonals, and so if Sir R----- could have picked all of the cards from any of these before the Baron, he should have won the game.
Unfortunately, this is exactly the same as a game of noughts and crosses, which every schoolchild knows cannot be won if the opposing player has their wits about them. Indeed, I explained as much to the Baron but I fear that he may not have entirely grasped its significance.
Given that a draw should have counted as a win for the Baron, I would most certainly have advised Sir R----- to decline the wager!
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