Can a cube pass through a hole cut in an equal-size cube?
In 1693, Prince Rupert of the Rhine wagered that a hole could be cut through a cube large enough to let a second cube of the exact same size pass all the way through it, without splitting the first cube into two pieces. Mathematician John Wallis proved the prince right. So just how much bigger could that second cube be, and still make it through?
Reveal the answer
Noticeably bigger than you'd guess. Wallis's original hole, cut along the cube's main diagonal, already lets an equal-size cube through with room to spare. About a century later, Dutch mathematician Pieter Nieuwland found a better-angled hole allowing a cube up to (3√2)/4 ≈ 1.06 times larger — a full 6% bigger — to slide through a unit cube. His solution was published posthumously in 1816. Mathematicians later showed all five Platonic solids share this 'Rupert property.'