Coin Rows

Eight counters lie in a row, each worth one to nine. You take one from the left end or the right end. A rival then takes one back, and it is never a mystery which: it always takes the larger end, and a tie goes to the left. Four turns each, the row empties, and you have to finish holding at least the target printed above the board.

The target is not a round number somebody chose. It is the exact total the best possible play collects on this row against that rule, worked out by the board before it showed you anything — so it is always reachable, and there is no slack in it at all. Take the wrong end once and the target becomes arithmetically impossible, which the board says out loud on the press that did it rather than leaving you to discover it four moves later.

That makes it a planning puzzle rather than a contest. Because the rival's rule is published and fixed, everything that happens next is a consequence of your own choices, so you can genuinely work the line out at the board. And the line is rarely the obvious one: the opening move is very often to hand over the smallest counter on the row, because of what that forces the rival to take next.

It runs entirely on your device: 0 network requests, works offline. No ads, no account, nothing to buy, and no betting, money or prizes of any kind.

1. Focus the board — click it, or press Tab until it is focused.
2. Read the two ends. Only the leftmost and rightmost counters can be taken. Everything between them is out of reach until the row shrinks to it, and the board marks each one so you always know which two are live.
3. Press the left arrow to take the left end, or the right arrow to take the right end. One press is one whole turn: your counter leaves the row and the rival answers immediately, so the row always comes back to you two counters shorter.
4. Press the up or down arrow to move the marker between the two ends, then Enter to take the one it names. Moving the marker is free — it changes nothing on the row — so you can point at an end and think before committing. The W, S, A and D keys mirror the arrows, and either shift key moves the marker too.
5. Watch "still gettable". It is the most you can collect from what is left, worked out fresh after every turn. Added to what you already hold it equals the target exactly, for as long as you are still on the best line. That is the number to plan against.
6. Think about what you leave, not what you take. The rival's next move is decided entirely by the two counters your take exposes. Taking the bigger end is what a beginner does, and it is usually wrong — you often want to give up a small counter so the rival is forced onto a middling one and leaves you the big one behind it.
7. There is no undo. The rival's rule is printed on the board and the whole row is visible, so everything you need in order to be sure was there before you pressed.
8. The round ends when the row empties, or the moment the target slips out of reach. Either way the board then shows the line that would have reached it, take by take.

You can play entirely by pointer instead: click either end counter to take it. Clicking anything else does nothing and costs nothing.

How do you decide which end of a row of numbers to take?

Not by size. Work backwards from what your take leaves behind. The rival's answer is forced — larger end, ties left — so each of your two options leads to exactly one position, and the question is really "which of those two positions is better for me?" That question has the same shape as the one you started with, on a shorter row, so it can be answered by solving the shortest rows first and building upwards: a two-counter row is trivial, a four-counter row is decided by the two-counter rows it can become, and so on to the full eight. Computer scientists call that an interval dynamic program, and the board runs exactly that table to set your target. At the board itself the practical version is shorter: look one full turn ahead — your take, then the rival's forced answer — and pick whichever of the two leaves you the better pair of ends.

Why does giving away the biggest counter often work?

Because the rival cannot refuse it. If you take the big end yourself, the rival is free to choose between whatever two counters you exposed, and it will help itself to the better one. If instead you take a small end and the other end is now the largest counter on the row, the rival is dragged onto it — but that is only bad for you if the counter it took was the one you wanted. It usually is not: the counters you actually want are the big ones sitting one place inside an end, and the only way to reach one is to make the rival remove the counter guarding it.

Is the target always possible?

Always, and by construction rather than by hope. The board fills the whole table of "best I can still collect from this stretch" before you see the row, and the target is simply the entry for the whole row. So a line that reaches it exists before the first press. It also has no margin — the target is the maximum, not a comfortable fraction of it — which is why a single wrong take ends the round. The board only deals rows where that matters: it throws away any row on which copying the rival's own rule would already reach the target, and any row with fewer than three genuine decisions on it, so every board you get has something to work out.

Is there any money, betting or in-app purchase in this?

None, and there never will be. The counters are counters — small numbered tiles used to keep score in a puzzle. There is no currency of any kind, nothing to buy, no prizes, no wagering and no way to stake anything on the outcome. Your results stay in your own browser.

Does it work offline, and can I play it with a keyboard or a screen reader?

Yes to all three. Once the page has loaded once, everything runs on your device — the generator that deals the row, the solver that sets the target, and the same solver again recomputing how much is still gettable after every turn. No server takes any part in play. The whole game is playable with the arrow keys and Enter alone, and every counter announces its value, whether it is an end, and who is holding it. Nothing is carried by colour: each counter also carries a symbol and a word, the two live ends are marked as such, and the running totals are written out in full.

What happens if I lose — do I find out what I should have played?

Yes, immediately. The round stops on the take that put the target out of reach, names that take and what it cost, and then prints the full line that would have reached the target: each of your four takes with the rival's forced answer after it. That is the point of ending the round early rather than letting you play out a row that can no longer reach the target — the correction arrives while you still remember the reasoning that produced the mistake.

Eight counters, always, each worth one to nine, so the whole row reads at a glance and the table behind it stays small enough to be exact rather than approximate. You move first and each side ends up with four counters. The rival plays one fixed published rule and never varies it; it is not an opponent that adapts, and it is not trying to beat you — it is the obstacle the puzzle is built around. There is no timer, no hint button and no undo. The target is the exact optimum with no margin, which makes this an unusually strict game: on most rows there is precisely one first move that works. Rows where the greedy reflex already succeeds are discarded rather than dealt, so the easiest kind of board here is one you will never see.

Trade Route is the other game here where a running total has to land on an exact figure and the answer is found by working backwards from the end. Route Plan is the one about reading the band of totals still reachable rather than the total so far, which is the same habit "still gettable" is teaching. Weight Split shows where the greedy rule is right and why. Stack Pops and Card Ladder are the other deals built by a solver before you see them, so no board is ever a dead end, and Balance Scale is the other puzzle about choosing the move that tells you the most rather than the move that grabs the most.

Bookmark this page (Ctrl+D, or ⌘D on Mac) or install the app — it works offline the next time you need it.