The Brick Factory

Where the question came from

“The work itself was not difficult; the trouble was only at the crossings. The trucks generally jumped the rails there, and the bricks fell out of them… the idea occurred to me that this loss of time could have been minimized if the number of crossings of the rails had been minimized. But what is the minimum number of crossings?”

1. Lay the rails yourself

Drag the kilns and the yards. Every crossing is marked. Try to reach the target — then try to beat it.

2. What was actually proven

The target comes from a formula found in the 1950s. This table shows it for each number of kilns and yards — and which entries people had managed to prove by 2026.

3. Eighty-two years

1. 1944The question. Turán, a forced labourer, asks it while pushing brick carts near Budapest.
2. 1950sDeclared solved. Zarankiewicz publishes the layout and a proof that it is the best possible.
3. Mid-1960sA gap. After about a decade as an accepted result, the proof is found to have a hole that nobody can fill.
4. 1970Six kilns. Kleitman proves the formula when one side has at most six.
5. 1993A few more, by computer. Seven kilns with eleven yards, and nine with nine, remain the smallest unsettled cases.
6. 2026A sixteen-page claim. A paper written by an OpenAI model claims every case, with a machine-checked statement. No specialist has yet verified it, and Wikipedia’s note on removing the claim reads: “let’s wait until we have published reliable sources.”