Core Module · How to Solve
How to solve Latin Squares
Latin Squares are the highest-accuracy section of the Core Module for most candidates — targets are 17–18 out of 20. The method is entirely systematic, and once you know it, there is no guessing.
WHAT IS A LATIN SQUARE?
One symbol per row, one per column — always
The dMAT uses 5×5 grids. Five letters (A–E) are arranged so that each letter appears exactly once in every row and exactly once in every column. You are given some cells pre-filled and must deduce the rest. No arithmetic. No guessing. Pure logic.
The two-step elimination method
Every Latin Square cell can be solved by combining exactly two scans:
STEP 1 — ROW SCAN
What letters are already in this row?
For any empty cell, look across its entire row. Record which of the five letters are already present. The missing ones are the only candidates for this cell.
Example
Row 3 contains: A, C, D → missing B and E.
The empty cell in row 3 can only be B or E.
STEP 2 — COLUMN SCAN
What letters are already in this column?
Now look down the column for the same empty cell. Which letters are already present in that column? Remove those from your row-scan candidates.
Example (continuing from Step 1)
Column 2 contains: A, B, D → missing C and E.
Intersection of {B, E} and {C, E} = E.
The empty cell at (row 3, col 2) must be E.
After you place one — rescan
Every time you fill a cell, you eliminate one option for every other empty cell in the same row and same column. Immediately rescan the affected row and column after each placement. A cascade of forced cells usually follows — the whole grid can dissolve in 20–30 seconds once you find the first forced cell.
ADVANCED — CONSTRAINT PROPAGATION
When no single cell is forced yet
Sometimes no individual cell has exactly one candidate. Instead of guessing, try this: for each letter, within a given row, how many cells could legally contain it? If a letter has only one possible position in a row, it must go there — even if that cell still has multiple candidates from the column perspective.
Example
In row 2, the letter D can only legally go in columns 1 or 4 (columns 2, 3, 5 already have D in their column). Now if column 1 already has D somewhere, column 1 is eliminated, so D must go in column 4.
This technique breaks deadlocks that simple row/column elimination cannot.
Timing strategy
The target is 17–18 correct out of 20 in 25 minutes (75 seconds per question). With practice:
- Easy questions (sparse grid, many givens): 20–30 seconds
- Medium questions (need 2–3 elimination steps): 45–60 seconds
- Hard questions (need constraint propagation): 75–90 seconds
If you've spent 90 seconds and have no forced cells, use your best guess and move on. Never leave a blank — wrong and blank both score 0.