A mathematical puzzle posed by Leonhard Euler in the 1700s has been resolved using quantum entanglement, according to new research.
Euler studied the problem of arranging officers of different ranks and regiments in a square grid so that each row and column contains each rank and regiment exactly once.
For a 6x6 grid, Euler concluded that no such arrangement exists, a conjecture proven correct in 1901.
He further believed the task was impossible for any grid of size 4k+2, where k is an integer.
That broader conjecture was disproved in 1959 when mathematicians found solutions for all such grids except the 6x6 case.
The new work demonstrates that if the officers are allowed to exist in quantum superpositions, entangled states enable a perfect arrangement even for the 6x6 grid.
The solution uses entangled quantum states to satisfy the constraints that classical arrangements cannot meet.
Researchers say the result reveals a fundamental link between quantum mechanics and combinatorial design theory.
Quantum entanglement is key to solving 250-year-old maths problem
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