How to Play Pentalpha

By Jaques of London · Est. 1795 · Updated 2026-08-17

Pentalpha is a single-player placement puzzle played on a five-pointed star drawn as five straight, overlapping lines creating nine distinct points. The challenge is deceptively simple to state but genuinely difficult to solve: place nine counters on the board one at a time, each following a strict movement rule, until every point is occupied. No point should be left empty and no rule broken.

Players love it because each attempt is quick, failure is instructive, and success feels earned rather than lucky. It travels easily, needs no batteries, and plays in a few quiet minutes. It is a natural fit for a tabletop or coffee table and works just as well scratched into sand as printed on card.

A little history

Pentalpha's origins are unclear. It is traditionally associated with the island of Crete, where a version of the board has been found scratched into ancient stonework, and the name combines Greek roots for five and alpha. Beyond that archaeological association, reliable documentation is thin. The game appears in various 19th and early 20th century puzzle collections under the same or similar names, which suggests it circulated widely across Europe before any single printed source codified it.

Setting up

1. Draw or lay out a five-pointed star so that five straight lines intersect to create exactly nine points: five outer points at the tips of the star and four inner points where the lines cross.
2. Ensure each of the nine points is clearly marked and large enough to hold one counter.
3. Place all nine counters beside the board. The board starts completely empty.

How to play

1. Pick up one counter from your supply. You must place it using the following rule on every single turn, with no exceptions.
2. Choose any empty point on the star as your starting point and set the counter there temporarily.
3. From that starting point, count two points along any one of the straight lines that pass through it. The middle point you pass over may be empty or already occupied; it does not matter. The point you land on at the end of the two-point move must be empty.
4. Move the counter from the starting point to that landing point. The counter is now placed.
5. If you cannot find any empty starting point from which a legal two-point move leads to another empty point, your attempt has failed. Remove all counters and start again.
6. Continue placing counters one at a time using the same rule until all nine counters are on the board. Each placed counter stays where it is for the rest of the attempt.
7. You may choose any eligible empty starting point on each turn; there is no fixed order. Choosing wisely is where the skill lies.

Winning and scoring

The puzzle is solved when all nine counters are on the board, one on each of the nine points of the star. There is no scoring system: you either succeed or you do not. Many players count the number of attempts needed to achieve a clean solution and try to reduce that number over time. A clean first-attempt solution is considered a genuine achievement.

The fine points

The most common point of confusion is whether the middle point of a two-point move needs to be empty. It does not. You are moving across that middle point, not placing a counter on it, so its status is irrelevant. The only requirement is that the starting point and the landing point are both empty at the moment of placement.

A second dispute arises over what counts as a straight line. The board has exactly five lines. A counter may only travel along one of those five defined lines in a single move; you cannot combine two lines or change direction mid-move. If a point lies at the intersection of two lines, a counter placed there can in future turns be treated as sitting on either line, but only one line is used per move.

How to win more often

• Start from an outer tip point on your first move. Tip points are served by only two lines each, so they become harder to reach as the board fills. Getting at least one counter onto each tip early keeps your options open.
• Think two moves ahead. Before placing a counter, check whether the move you are about to make will leave your next counter with at least one legal landing spot.
• Avoid clustering counters on adjacent points too early. Dense clusters block legal moves and tend to leave isolated empty points that cannot legally be reached.
• The four inner intersection points are each served by multiple lines and are easier to reach late in the game. It is usually sound to leave at least one or two inner points empty until the final placements.
• If you are stuck with two or three counters still to place, retrace your last two or three moves in your head before clearing the board entirely. Often a single earlier choice was the point of failure, and adjusting just that one move solves the puzzle.

Variations

Timed challenge

Set a timer for three minutes and attempt to solve the puzzle before it runs out. This adds light pressure without changing any rule. Players competing informally can each take a turn against the clock and compare the number of successful solves in a fixed number of attempts.

Partial board

For a gentler introduction, play with only seven or eight counters rather than nine. The final one or two points are left empty, making a full block-out less likely and giving beginners a chance to learn the movement rule without repeated frustration.

Named-start constraint

Before beginning, nominate one specific point on the star where the first counter must be placed. This removes one degree of freedom and meaningfully changes which solutions are available, offering a fresh challenge once the standard puzzle has been solved several times.

Competitive attempts

Two players each have their own board and identical set of nine counters. Both attempt the puzzle simultaneously. The first to place all nine counters legally wins the round. Best of five rounds decides the match. All rules remain the same; the variation is purely the head-to-head format.

Pentalpha: frequently asked questions