A Journey in Three Cities · By the Numbers
Three cities. Three locks. One open road.
New York counts in coins. London counts in squares.
Vienna lets the numbers run until they settle.
Nothing here asks what you know —
only what you can work out.
The cab idles in traffic and the meter ticks. The driver, who clearly enjoys a riddle more than a fare, hands you a receipt with four lines on it — each line a small sum. "Work each one out," he says, "then trade every total for a letter, the old schoolyard way: 1 is A, 2 is B, all the way to 26 is Z. Read the four letters top to bottom and you'll know who's waiting for you in the harbour."
The receipt names a person — the one who has watched over the harbour since 1886. The lock wants her common name.
Your bag is in a locker, and the locker has a nine-digit code. The attendant won't simply tell you — he points to a half-finished grid pinned behind the counter. "Fill it in proper," he says. "A full nine-by-nine. Every row holds 1 through 9 once, every column the same, and each of the nine 3-by-3 boxes the same again. When it's done, read the nine teal squares straight down the diagonal — top-left corner to bottom-right. That string of digits is your code."
The nine diagonal digits, in order, are the locker code. Solve it fully — nothing will tell you whether a single cell is right until the whole code is entered below.
The great wheel turns over the Prater, and the old operator has one last game. "Take the first four digits of the code you carried from London," he says. "Arrange those four into the largest number you can, then into the smallest. Subtract the small from the large. You'll have a new four-digit number — pad it with a zero in front if it falls short. Do the very same thing again to that. And again. The wheel keeps turning until it stops turning — and it always stops on the same spot."
It takes only a few turns. When the wheel finally rests, the same four digits come up no matter where you began — that fixed number is what the final lock wants.
Three cities, three locks — all open. The road is clear.
In New York you totalled four cab-meter lines — 12, 1, 4, 25 — and traded them for letters to find LADY, the one who has watched the harbour since 1886.
In London you solved the full nine-by-nine and read its teal diagonal top to bottom: 185279634.
And in Vienna you took its first four digits — 1852 — and set them turning, 8521 − 1258 and on through six turns, until the wheel rested where it always rests: 6174, Kaprekar's constant, the number every four-digit road leads home to.
"All journeys are arithmetic in the end —
you only ever subtract the place you left from the place you arrive."
— a note left in gondola 13