Meet the Millers, George and Roxanne, proprietors of the world’s largest collection of mechanical puzzles: physical objects that a puzzler holds and manipulates while seeking a solution. In total, the Miller collection — an accumulation of collections, and collections of collections — amounts to more than 80,000 puzzles. It comprises some five thousand Rubik’s Cubes, including a 2-by-2-by-2 rendering of Darth Vader’s head. And there are more than 7,000 wooden burr puzzles, such as the interlocking, polyhedral creations by Stewart Coffin, a Massachusetts puzzle maker; they evoke a hybrid of a pine cone and a snowflake and are Mr. Miller’s favorites. Mrs. Miller is fond of their 140 brass, bronze and gold puzzle sculptures by the Spanish artist Miguel Berrocal; Goliath, a male torso in 79 pieces, is “a puzzle that all puzzlers lust after,” she said.

Until recently, the Miller collection resided at Puzzle Palace in Boca Raton, Fla., filling their mansion and a museum (a smaller house) next door. Puzzles occupied even the bathrooms. Then last year, on a whim, the Millers bought a 15th-century, 52-room castle in Panicale, a hamlet in central Italy. They packed their puzzle collection into five 40-foot shipping containers and, for their own transit, booked a cruise from Miami to Rome.

Before sailing away in April, the Millers went on a two-month road trip — “a last hurrah,” Mr. Miller called it — visiting puzzler friends from coast to coast. Along the way they accumulated more puzzles. In Garden Grove, Calif., they loaded up a cargo van with 58 boxes from Marti Reis, who donated her collection of folksy punning puzzles by the designer RGee Watkins, such as Diamond Ring, a dime with a metal ring passing through the coin’s center. The puzzle maker Lee Krasnow, who has production facilities in Portland, Ore., and Grand Rapids, Mich., met the Millers at a puzzle party on the outskirts of Austin, Texas, and hand-delivered his famed Clutch Box. Made from exotic hardwoods and precision machined metals, it opens with a subtle unlocking mechanism; the goal is simply “the thrill of having opened it,” Mrs. Miller said. And then, “if you’re daring,” Mr. Krasnow added in an email, the goal is “to fully disassemble it into about 40 individual pieces.”