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Hours from anywhere, a family has run out of ways to pass the time. Then someone notices the little green mile markers by the road, one every mile, each with its own number.
"New game," says the driver. "Marker 1 is worth a whole dollar, marker 2 half a dollar, marker 3 a third, marker 4 a quarter, and so on. Call out markers that add up to exactly one dollar and you win."
Marker 1 on its own is banned as too easy, and no marker may be picked twice. After that the car goes quiet for a good long while. That silence is what this page is about: the family's game sits very close to Erdős Problem 289, a real mathematical question that stayed open for almost fifty years. Four screens from now you will be looking at it.
Mile marker n is worth 1n of a dollar.
Pick markers, each at most once, so that their values add up to exactly one dollar. No rounding: 99.9 cents is a loss.
Over the next screens the game gets harder step by step, and the mathematics appears on the right, one piece at a time. The last screen shows Erdős Problem 289 itself, as Erdős and Graham posed it in 1980, and the 2026 answer.