The new coins are pouring off the press faster than anyone can count them, and the warden of the mint, pixel Isaac Newton, has decided to check every tray himself. Each tray hides pairs of coins, keys, ledgers and seals, and only a matched pair may leave for the strongroom. The clerks call the nightly count the Tumbling Ledgers.
The trays are stacked on a slanted rack, so whenever a pair is lifted out, everything above it slides down to fill the gap. A card remembered at the top may land two rows lower, and pixel Newton, who knows a thing or two about falling objects, follows every drop. Clear a tray and a bigger one arrives. When the clock runs out, the mint closes for the night. How many trays can be counted?
