A practical guide to Sos intersection puzzles

Sos is a letter-placement logic puzzle built around the letters S, O and Z. Rather than placing a number in every cell, the solver works from clues attached to grid intersections. Each clue gives a local count: the letter named by the clue must occur a stated number of times among the cells touching that point. The completed grid must satisfy every clue and any letter totals printed with the puzzle.

This is a propagation puzzle rather than a guessing game. Read one clue, list the placements it allows, and use neighbouring clues to narrow them. For Australian readers, Zagonetka.net provides Croatian and international material that can be harder to find through a local newsagent or in the wider Australian puzzle-book market.

Read the clue at the point it marks

The first habit is to separate position from content. At an interior intersection, four cells meet; where a clue sits on an outer boundary, only the cells actually touching that point matter. Circle the relevant cells before entering letters. A clue is not attached to its upper-left neighbour, even when that square looks like the natural place for it.

Next, translate the clue into a plain statement. If it calls for two S cells, the touching set must contain exactly two S cells. The other letters can occupy the remaining cells, but the count applies only to the named letter. Writing “S = 2” beside the point prevents confusion between the clue’s letter and the letters eventually entered in cells.

Keeping this local view makes a crowded grid manageable. On a Melbourne tram, each stop matters more than the length of the whole route; likewise, a careful reading of four touching cells is more valuable than an unsupported glance across the board.

Begin with the most constrained intersections

Work first on clues with the fewest legal outcomes. A zero count removes the named letter from every touching cell. A count equal to the number of available cells fixes all of them. A one-cell boundary clue may settle that cell immediately, provided the boundary reading is correct.

For an interior clue, compare candidate sets directly. A count of one allows four choices of cell; a count of two allows six pairs; a count of three allows four choices for the non-matching cell. These small sets are easier to test than a whole row, so keep them visible until another clue intersects them.

Do not commit merely because a candidate looks attractive. Ask whether every overlapping clue can still be met. If two clues disagree with a choice, remove it. If only one choice survives, that is a forced placement and is safer than a plausible guess.

Turn overlapping clues into forced placements

Two intersection clues often share cells, and that overlap is where useful deductions appear. If a shared cell cannot be S under one clue, reject S there immediately. If it cannot be O or Z elsewhere, its value may become forced even before either clue has been solved in full.

The mark-and-propagate routine also appears in star battle strategy, where one certain placement can unlock several others. The same discipline works here: update all affected candidate sets after every placement, then scan those sets for a new restriction. Each deduction should remove possibilities, not merely add confidence.

In a dense Sydney grid, one street can be reached from several directions. A puzzle cell behaves similarly when two clues constrain it from different angles. Reading those constraints together often reveals the obvious letter that neither clue reveals on its own.

Keep two compact checking lists

Use this order during the first scan:

Use this list before declaring the puzzle solved:

The two lists separate progress from proof. The first improves efficiency; the second catches transcription slips and overlooked boundary cases. That habit suits the show-your-working culture of mathematics events such as the Australian Mathematics Competition, where a clear check is part of a convincing solution.

Finish with an independent verification pass

After filling the grid, put the original clues beside it and verify without relying on earlier annotations. For each point, identify the relevant cells afresh, count the named letter, and compare the result with the clue. This catches errors caused by carrying a mistaken cell set through several deductions.

Then check the puzzle from the opposite direction. Instead of asking which letter belongs in a cell, ask whether a chosen letter violates a count at any intersection. Apply the same test to every boundary clue, since these often use fewer cells and are easily counted from the wrong side.

Short verification bursts also fit a busy AFL weekend: ten minutes after lunch can catch a mistaken count without turning the whole solve into another marathon. A completed Sos grid must be both full and consistent: every intersection clue must agree with the letters actually touching it, and every global letter requirement must hold. That double agreement is the finish line.