Thinking Skills
The diagram shows a 6×6 grid of equal cells. A cell is shaded when row + column (counting from 1 in the top-l…
Question 1 · Multiple choice
Question
The diagram shows a 6×6 grid of equal cells. A cell is shaded when row + column (counting from 1 in the top-left) is even; otherwise it is unshaded.
Options
How many shaded cells are there in total?
- A.16
- B.17
- C.18
- D.19
Correct answer
Explanation
Step 1: Understand the shading rule.
A cell is shaded when (row number + column number) is even. Using a few examples in Row 1:
| Row | Col | Row+Col | Even? | Shaded? |
|---|---|---|---|---|
| 1 | 1 | 2 | Yes | ■ |
| 1 | 2 | 3 | No | □ |
| 1 | 3 | 4 | Yes | ■ |
| 1 | 4 | 5 | No | □ |
This creates a checkerboard pattern — every other cell is shaded, starting shaded in Row 1.
Step 2: Count shaded cells row by row.
In a 6-column row, exactly 3 out of 6 cells are shaded:
| Row | Pattern | Shaded |
|---|---|---|
| Row 1 | ■ □ ■ □ ■ □ | 3 |
| Row 2 | □ ■ □ ■ □ ■ | 3 |
| Row 3 | ■ □ ■ □ ■ □ | 3 |
| Row 4 | □ ■ □ ■ □ ■ | 3 |
| Row 5 | ■ □ ■ □ ■ □ | 3 |
| Row 6 | □ ■ □ ■ □ ■ | 3 |
Step 3: Find the total.
Total shaded = 6 rows × 3 shaded per row = 18 cells
(This is also exactly half of the total 36 cells, which always happens on an even × even checkerboard.)
Answer: 18
