Amsterdammed

Where Amsterdammed comes from

Amsterdammed is our take on the simple loop puzzle, the most stripped-down member of a family the Japanese publisher Nikoli has been refining for decades. The family patriarch is Slitherlink, first printed in 1989: draw one closed loop on a grid, guided by number clues. Dozens of loop-drawing variants followed — Masyu swapped the numbers for pearls that force turns and straights — and the simple loop is what remains when you take away every clue entirely. No numbers, no pearls: just open squares the loop must visit and blocked ones it must avoid. Mathematicians know the underlying object as a Hamiltonian cycle, a closed tour visiting every point exactly once — famously hard in general, and famously satisfying when a well-built grid makes it fall to pure reasoning. Amsterdammed dresses that abstraction in a city that was asking for it: one continuous canal, threading every open square and closing back on itself, the way water in Amsterdam always finds its way around.

How to get better at Amsterdammed

Count to two, everywhere. The entire puzzle hangs on one number: every open square touches the canal exactly twice. So any square with only two available borders is finished before you start — corners always, and any square pinned between houses and walls. Sweep the whole board for these before drawing anything speculative.

Make the X do the work. The moment a square has its two canal segments, its remaining borders are dead — mark them. Each X shrinks a neighboring square's options, and when a neighbor drops to two open borders, its path is forced too. Strong solvers lay X's as eagerly as canal; the marks are how one certainty becomes a chain of them.

Read corridors at a glance. A one-square-wide channel between blocks gives the water no choice: straight through, both ends forced. Long corridors are free progress — trace them first and let the ends of each corridor seed the harder open country.

Watch for the early close. A loop that seals itself before covering every open square is wrong, however legal each segment looked. When two long canal ends drift toward each other, check what's left stranded outside before joining them — the join that's forbidden tells you the path must detour, which is itself a deduction.

Respect the dead-end test. If marking a border X would leave any square with fewer than two ways in, that border must carry canal. Run this test on stubborn squares mid-solve; it's the contrapositive of the counting rule, and it cracks the middles of the roomy weekend boards.

Use the week. Monday's 5×5 teaches the forced-corner grammar in two minutes; Sunday's boards, up to 9×10, chain those same deductions thirty moves deep. Same rules, longer sentences.

A round in the life

Thursday, a 7×7 with a clump of row houses off-center. You take the corners first — four squares, eight forced segments, no thought required. Then the square wedged between two houses on the top row: blocked left and right, so the canal must enter from below and run along the top. Two more segments, and an X on the border it can't use — which leaves the next square over with exactly two open borders, forced too. Across the board, your two longest ends begin curling toward each other, but joining them now would strand the far column outside the loop. So the join is forbidden, the detour is forced, and the water bends obediently north. You haven't guessed once. The loop closes itself; you were just holding the pen.