Arcana Chain — One hundred boards, one unbroken chain

What is Arcana Chain — One hundred boards, one unbroken chain

Arcana Chain empties a board one card at a time. Every card you take must be one rank above, one rank below or the same rank as the last, and on most boards Ace and King close the circle. Grids run from a nine-card 3x3 to the forty-nine-card 7x7. What squeezes you is the move budget: one move per card, one more per frozen card, plus a thin margin — three spare on level 1, two until level 30, one until 64, none at all on many of the last ones.

Each board is dealt along a Hamiltonian path: the generator shuffles a snake that visits every cell with reversals that cannot break it, then writes the ranks along that route. A chain touching every card therefore always exists, and since the route walks the grid, consecutive links are neighbouring cells. Over it sit frozen cards that cost a move to crack, chained cards that need a neighbour removed first, wilds that free the next pick, and bombs whose fuse drops on every move. A hundred levels in ten chapters, from First Deal to Arcana Master.

How to play

1. Click or tap any card to open the chain. After that each pick must stay within one rank of the last, and a warning at the start says when Ace and King do not connect.
2. Frozen cards take two taps: the first cracks the ice for five points and one move. Chained cards open only when a card beside them is removed — thawing a neighbour does not count.
3. Wilds can be taken at any moment and leave the next pick free. Bombs carry a fuse that falls by one on every move, thaws included; at zero the level ends.
4. Moves is your whole budget. Hint, three per level, lights the next link of the built chain; Undo, also three, rewinds a move and its points.

Strategies that work

• Take the neighbour. The route a level is dealt along always steps to a card touching the previous one, so when three cards match your rank, the one beside your last pick is almost always the true link. The long jump scores the same and usually strands two cards in a far corner.
• Work out your margin before the first tap: moves, minus cards left, minus frozen cards. Level 1 gives 12 moves for 9 cards; the daily board of 26 August, 37 for 30 cards and six blocks of ice; level 100, exactly 62 for 49 cards and 13 of ice — not one tap spare.
• Read the fuses first. A bomb's number is its place in the built chain plus about three moves of grace, so one showing 6 belongs to the third or fourth link, while a 32 on a 25-card board can wait until the end.
• Bombs pay twenty a card instead of ten and still multiply by the combo, so reaching one at ×9 is worth 180 against 40 at ×2. Never trade the fuse for the multiplier: a lost level still posts your points, with no stars.
• The combo beats a tidy finish. Cards score ten times a combo that climbs to ×9 and falls back to 1 after six seconds without a move, so one long stare costs 360 points — the whole end bonus is 25 per saved move plus 100, at most 175.

A little history

Arcana Chain was written for puzzle-me.com and has no direct ancestor. Two old ideas meet in it: the patiences where a card is played on one a rank above or below, turning a tableau into a single chain, and the Hamiltonian path, a route visiting every vertex of a graph exactly once. Hard to find in general, it comes free on a rectangular grid, where a snake is already one and a backbite shuffle rearranges it without cutting it. Every level is built backwards from that route, so a solution is guaranteed: a thousand generated levels were checked, all solvable inside budget.

Frequently asked questions