Symbol Grid
Symbol Grid is pure deduction. A square grid follows one rule, each symbol exactly once in every row and every column, and you must say which symbol belongs in one highlighted cell. Nothing is hidden and nothing is probable: the clues force exactly one answer every time. If you find yourself guessing, the move you need is one you have not made yet, and this lesson teaches both of them.
What you see
A square grid of 4, 5 or 6 rows and columns. Some cells hold a symbol (the clues); the rest are blank. One blank cell has an accent border and a question mark: the highlighted cell, which is the one you answer. Its row and column are highlighted so you can scan them quickly. Rows are numbered down the left and columns across the top, and the highlighted row's and column's numbers are drawn in the accent colour.
The symbols are solid shapes: circle, square, triangle, diamond, star and hexagon. A grid of size n uses the first n of them, so a 4 by 4 grid uses circle to diamond and a 6 by 6 grid uses all six.
Below the grid is a row of answers, one button per symbol, numbered 1 to n. Click an answer or press its number key and the symbol appears in the highlighted cell; you can change it until you press Check answer (or Enter). After the check the cell turns green with the right symbol, and if you chose a symbol that already sits in the highlighted row or column, that symbol is outlined in red. You only answer the highlighted cell. The other blank cells stay blank; you fill them in your head only when that helps you reach the highlighted cell.
How a puzzle is built
The generator starts from a complete, valid grid (a Latin square), shuffles its rows, columns and symbol names, and picks the cell to highlight. It then removes clues one at a time, keeping each removal only if the highlighted cell's value is still forced. Whenever quick deduction cannot confirm that, it runs an exhaustive search over every possible completion of the grid. The result is guaranteed: across all valid ways to complete the grid, the highlighted cell can hold only one symbol.
The generator also measures how the highlighted cell can be reached, using two standard moves (explained in the method section) applied in rounds. The number of rounds needed is the trial's depth.
| Level | Grid | Share of cells given | Depth of the highlighted cell | Other requirements |
|---|---|---|---|---|
| 1 | 4 by 4 | 70–95% | 1 | |
| 2 | 4 by 4 | 60–85% | 1–2 | |
| 3 | 4 by 4 | 35–60% | 2–3 | highlighted row and column stripped first |
| 4 | 5 by 5 | 55–80% | 1–3 | |
| 5 | 5 by 5 | 45–70% | 2–4 | at least one hidden single; row and column stripped first |
| 6 | 5 by 5 | 40–60% | 3–6 | at least one hidden single; stripped first |
| 7 | 6 by 6 | 45–65% | 2–5 | at least one hidden single; stripped first |
| 8 | 6 by 6 | 35–55% | 3–8 | at least two hidden singles; stripped first |
| 9 | 6 by 6 | 30–55% | 4 or more | two hidden singles; may need case analysis |
| 10 | 6 by 6 | 25–55% | 5 or more | two hidden singles; may need case analysis |
"Stripped first" matters more than anything else in the table. At level 3 and from level 5 upwards, the generator removes clues from the highlighted cell's own row and column before touching the rest of the grid. The obvious place to look therefore contains the least information, and the answer has to be carried in from cells elsewhere.
What it measures
Symbol Grid measures deductive reasoning: chaining given constraints to a conclusion that must be true. It is the only game in the deduction facet of your reasoning score and carries 13 per cent of the reasoning dimension. A smaller part of its load is planning: choosing which cell to settle first so that the chain reaches the highlighted cell.
Latin squares are old mathematics. The name comes from Leonhard Euler, who used Latin letters as the symbols; the Korean mathematician Choi Seok-jeong had published examples decades earlier. Every completed Sudoku is a Latin square with an extra box constraint. The number of possible squares grows fast: 576 of order 4, 161,280 of order 5 and 812,851,200 of order 6.
The research task closest to this game is the Latin Square Task of Birney, Halford and Andrews. It uses a 4 by 4 grid of geometric shapes with the same single rule, and was designed to vary one thing: relational complexity, the number of cells whose values have to be combined in one step to settle a cell. Because the rule is simple and the content is abstract, performance reflects reasoning capacity rather than knowledge. Hearne, Birney and Mattingley replicated the design and found that error rates and response times rose sharply with relational complexity, and that the task was reliable within and across testing sessions.
How it is scored here
Each trial is correct or incorrect. There is no partial credit, because there is only one answer and it is always forced.
The trial's measured difficulty comes from the depth (one point per round), plus 1.2 points for each step of grid size above 4 by 4, plus 2 points when the highlighted cell cannot be reached by the two basic moves alone. Such trials count as depth 8. So a 6 by 6 trial at depth 4 rates about 6.4, and a case-analysis trial on a 6 by 6 grid rates the maximum.
As in all reasoning games here, accuracy carries 85 per cent of each trial's value and speed relative to the expected time at that difficulty carries 15 per cent. Each trial's value is scaled by its difficulty, and your score compares that with a reference in which 50 means you are performing at the level your working difficulty predicts. You start at level 3; a correct answer moves the next trial up a level and a wrong answer moves it down.
The profile shows four diagnostics for this game: the deepest chain of deductions you have completed correctly, your deductions per second, the share of case-analysis trials you solved, and the extra time each additional step costs you. The session report explains each trial: how many forced steps settled the highlighted cell, or that it could not be settled by the basic moves alone.
Where you will meet it
Latin-square grids are one of the few reasoning formats that appear almost unchanged in game-based assessments.
Publicly reported uses. Formats change, so check the latest invite you receive.
- AonDeductive-logical thinking (gapChallenge): use logic to fill the empty cell to complete the pattern, 6 minutes
- CapgeminiCandidates report a deductive-logical game: an N by N symbol grid where each row and column holds every symbol once
The same deduction drives arrangement puzzles in written tests: seating plans, schedules and the logical-reasoning sets in CAT's DILR section, where a table of people and attributes has to be completed from constraints. AMCAT lists puzzles and decision tables among its deductive topics. Symbol Grid strips those down to the rule itself, so it trains the move without the reading.
The method
Two moves settle almost every cell. Learn to see both.
- Naked single
A blank cell whose row and column between them already contain every symbol but one. The cell must hold the missing symbol.
- Hidden single
A symbol that has only one possible place left in a row (or column), because every other blank cell in that line already sees the symbol in its own column (or row). The symbol must go there, even if that cell has several candidates on its own.
- List the highlighted cell's candidates
Read the highlighted cell's row, then its column, and cross off every symbol you see. Whatever is left is the candidate list. If one symbol is left, you are done.
- Ask where each candidate could go instead
For each remaining candidate, look along the highlighted cell's row: can that symbol go in any other blank cell of the row? A blank cell is ruled out if its column already holds the symbol. If no other cell can take it, the highlighted cell must. Repeat along the highlighted cell's column.
- Settle a helper cell
If the highlighted cell still has two or more candidates, find a blank cell in the highlighted cell's row or column that has only one candidate, or a symbol with only one home in a line that crosses them. Fill it in your head and return to step 1. Each helper you settle removes one more candidate somewhere.
- Follow the chain outwards
At deep levels the helpers themselves need helpers. Work outwards from the highlighted cell: which cells, if settled, would change the highlighted cell's row or column? Settle those first, not whichever cell happens to be easiest.
- When the moves run out, test a hypothesis
On the rare level 9 and 10 trials that need case analysis, suppose the highlighted cell is candidate X and follow the consequences. If they force two identical symbols into a row or column, or leave a cell with no candidate, X is impossible. When only one candidate survives, that is the answer.
Worked example 1
Show the solution
Candidates. The highlighted cell is row 2, column 3. Row 2 holds a circle. Column 3 holds a square and a circle. Crossed off: circle, square. Candidates: triangle or diamond.
Hidden single. Where else could a diamond go in row 2? Column 1 has a diamond (row 3), so R2C1 cannot take it. Column 2 has a diamond (row 4), so R2C2 cannot. R2C4 is already a circle. The only home left for the diamond in row 2 is the highlighted cell.
Answer: diamond.
You can also get there the other way round. R2C2 sees a circle in its row and a square and diamond in its column, so it must be a triangle. That leaves the highlighted cell with only the diamond. Both routes are valid; the hidden single is one step shorter.
Worked example 2
Show the solution
Candidates. The highlighted cell is row 3, column 3. Row 3 holds only a square. Column 3 holds a circle and a triangle. Crossed off: square, circle, triangle. Candidates: diamond or star. A naked single is not available.
Hidden single on the star. Where can the star go in row 3? R3C1 cannot: column 1 has a star in row 1. R3C2 cannot: column 2 has a star in row 4. R3C4 cannot: column 4 has a star in row 2. R3C5 is already the square. Every cell except the highlighted cell is ruled out.
Answer: star.
Notice what made this work. None of the useful information was in the highlighted cell's row or column; it was in the stars scattered across the other columns. That is the pattern you will see from level 5 onwards: search by symbol, not by cell.
Tips and traps
Guessing habits
- Scan the whole grid hoping something jumps out
- Pick between the last two candidates by feel
- Try to complete the entire grid
- Look only in the highlighted cell's row and column
Deduction habits
- Start from the highlighted cell: list its candidates first
- Find the fact that eliminates one of them
- Settle only the cells that bear on the highlighted cell
- Search symbol by symbol across every column
Levelling up
The main steps up are the change of grid size at levels 4 and 7, and the stripping of the highlighted cell's row and column at levels 3 and 5. On a 6 by 6 grid, every candidate list is longer, and every hidden single involves checking more columns.
- Levels 1 to 2. Most highlighted cells fall to the candidate list alone. Use them to make the row-plus-column check automatic.
- Levels 3 to 6. Expect one or two hidden singles. Train the symbol-by-symbol search.
- Levels 7 to 8. Chains of three to eight rounds. Before you settle anything, ask which cell would change the highlighted cell's candidates if it were filled.
- Levels 9 to 10. Some trials cannot be settled by the two moves. Pick the candidate you suspect is wrong and look for the contradiction it causes. A hypothesis that survives a few steps is not proof; only the contradiction counts.
- Week 1
- Three sessions of 10 to 15 trials
- On every trial, say the highlighted cell's candidate list before anything else
- After each miss, find which clue you overlooked
- Week 2
- Practise the hidden single on purpose: on every trial, ask where each candidate could go in the row and column
- Hold level 5 and above
- Time yourself only after accuracy is steady
- Week 3
- Work towards 6 by 6 grids at levels 7 to 8
- Before filling any helper cell, name why it matters to the highlighted cell
- Mix in one SwapCode session for a different kind of deduction
- Week 4
- Short timed runs of six minutes to match game-based rounds
- Review the session report for trials needing case analysis
- Rest before the real test
Check yourself
- On a 5 by 5 grid, the highlighted cell's row contains a circle and a star, and its column contains a star and a square. How many candidates does the highlighted cell have?
- What is a hidden single?
- At level 6 you have narrowed the highlighted cell to two candidates and see no way to decide. What does the design of the game tell you?
and 2 more
Sources
- Birney, D. P., Halford, G. S., & Andrews, G. (2006). Measuring the influence of complexity on relational reasoning: The development of the Latin Square Task. Educational and Psychological Measurement, 66(1), 146–171. doi:10.1177/0013164405278570
- Hearne, L. J., Birney, D. P., & Mattingley, J. B. (2020). The Latin Square Task as a measure of relational reasoning: A replication and assessment of reliability. European Journal of Psychological Assessment, 36(2). doi:10.1027/1015-5759/a000520
- Latin square. Wikipedia. en.wikipedia.org/wiki/Latin_square
- Aon. Prepare for your online assessment: logic tests. aon.com
- GameAssessmentPrep. Capgemini game-based test: games and rounds (candidate reports). gameassessmentprep.com/employers/capgemini
- AMCAT. AMCAT syllabus: Logical Ability. myamcat.com/amcat-syllabus
- Common Admission Test. Wikipedia. en.wikipedia.org/wiki/Common_Admission_Test
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