Dot Situation: Mental Ability Test (MAT) Notes for NMMS

Dot Situation – NMMS MAT Study Notes

NMMS – National Mental Mathematics Scholarship
MAT – Mental Ability Test
Topic – Dot Situation

1. Simple Explanation

A dot situation is a puzzle where a regular grid of dots is filled with a certain number of blank (empty) dots.
The goal is to find the number of filled dots that satisfy the conditions given (usually “all rows, columns, and sometimes diagonals have the same number of filled dots”).

Typical format:

+---+---+---+   ← 3×3 grid
| • | • | • |
+---+---+---+
| • |   | • |
+---+---+---+
| • | • | • |
+---+---+---+

Here the “•” are filled dots; the “ ” (blank space) is an empty dot.
In the example, one dot is missing – the question might ask: How many dots are missing? or Which dot is missing?

The key is that the arrangement must satisfy a pattern rule (e.g., each row/column/diagonal has the same number of filled dots).

2. Key Points to Remember

#	Concept	Why It Matters
1	Grid Size	3×3, 4×4, 5×5 etc. Count rows/cols to know total dots.
2	Pattern Rule	Usually “each row, column, and sometimes the two main diagonals must contain the same number of filled dots.”
3	Missing Dots	Find which dots violate the rule – those are the blanks.
4	Counting	Count filled dots in each row/col/diag. Compare with others.
5	Symmetry	Many dot situations exploit symmetry – check mirrored rows/cols.
6	Process of Elimination	If one row has fewer dots, the missing dot must be in that row.
7	Options	Often given as multiple‑choice – check each option quickly.
8	Time Management	Allocate ~20–30 seconds per problem; skip if too complex.

3. Worked Example

Problem

+---+---+---+
| • |   | • |
+---+---+---+
| • | • | • |
+---+---+---+
| • | • | • |
+---+---+---+

Each row and each column should contain the same number of filled dots. How many dots are missing and where?

Step‑by‑Step

Identify the pattern rule
Each row and column must have the same number of filled dots.
Count current dots
- Row 1: 2 dots
- Row 2: 3 dots
- Row 3: 3 dots
Columns:
- Column 1: 3 dots
- Column 2: 2 dots
- Column 3: 3 dots
Determine the target count
The majority of rows/columns have 3 dots.
So the correct count per row/column is 3.
Find deficits
- Row 1 has 2 → missing 1 dot.
- Column 2 has 2 → missing 1 dot.
Locate the missing dot
The only intersection of Row 1 and Column 2 is the middle dot (row 1, column 2).
Therefore the blank must be there.
Answer
One dot is missing, at the position (row 1, column 2).

4. Quick Revision Summary

Item	What to Check	Tip
Grid size	Total dots = n×n	Write it down quickly.
Pattern rule	Same number of filled dots per row/col (±diagonals)	Identify rule first.
Count each row/col	Compare counts	Use a quick tally.
Identify deficits	Rows/cols with fewer dots	Those are candidates for blanks.
Locate intersection	Cross‑check deficits	The missing dot is at the intersection.
Verify diagonals	If rule includes them	Count diagonal dots too.
Time‑saver	Skip if pattern unclear	Move on and return if time allows.

Practice Tip

Draw a 3×3 grid on paper, fill 8 dots (one missing), and try to deduce the missing position using the steps above. Vary the missing positions to see how the pattern changes. This will reinforce the elimination process and speed up your solving time.