The windowsill above the sink is where my wife and I place our dirty wine glasses. And while both of us love each other, neither of us love loading the dishwasher. As a result, these dirty glasses accumulate en masse on the windowsill until there is physically no room left to place another.
For a while, it was simply up to chance who would wind up having to do this chore. But over a period of months, without either of us having spoken of the matter aloud, my wife and I found ourselves embroiled in an intensely competitive game of strategy, complete with rules of fair play. The first such rule was that whosoever found themself unable to place another glass on the windowsill must concede defeat, and load the dishwasher with all the glasses. The second such rule was that any glasses already placed would under no circumstances be disturbed until the washing. The third such rule was that we would rigidly adhere to a previous habit of ours, that of myself retiring my emptied glass of wine after dinner, and of my wife nursing her drink until later in the evening. We would dirty no other glasses during the day.
As such, I conspired a strategy to escape the chore entirely: When the windowsill was empty, I would place a glass in its center, and then precisely mirror each of her subsequent placements. I won each and every game.
My wife wasn't a fan of this strategy, but she wasn't about to admit defeat. Her riposte took the form of her feigning adoration for a truly dreadful potted plant she had found and purchased at the market, and then placing it, conspicuously off-center, right there on our windowsill gameboard. Her motive was obvious, but for its creativity I deemed it would be unsporting on my part to call her foul. Thus, a silent addendum to the rules: The plant would never be moved. (Nor would it be watered, but that was the result of an unrelated dispute between us.)
Alas, I must now seek counsel from greater puzzlers so that I might escape an equal division of labor. How do I defeat my wife in this new game, what should be my strategy? The dimensions of the windowsill, glasses, and plant are as follows:
- The windowsill is 82 inches wide (why yes, it is very large and impressive)
- The glasses are identical, each 4 inches in diameter
- The potted plant is 8 inches in diameter, placed 51 inches from the left of the windowsill
To be clear, intervals are continuous, not discrete: We are allowed to place glasses freely, not merely in a whole number of inches from the right or left.