CAT 2024 Slot 2 — DILR Question 8
Answer the following questions based on the information given below.
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below.
| Column 1 | Column 2 | Column 3 | Column 4 | |
|---|---|---|---|---|
| Row 1 | □ | □ | □ | □ |
| Row 2 | □ | □ | □ | |
| Row 3 | □ | □ | ||
| Row 4 | □ |
(Row 1 has 4 slots in Columns 1–4; Row 2 has 3 slots in Columns 2–4; Row 3 has 2 slots in Columns 3–4; Row 4 has 1 slot in Column 4 — ten slots in all.)
1. Numbers in any row appear in an increasing order from left to right.
2. Numbers in any column appear in a decreasing order from top to bottom.
3. 1 is placed either in the same row or in the same column as 10.
4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
6. 4 and 6 are placed in the same row.
For how many slots in the grid, placement of numbers CANNOT be determined with certainty?
Answer & solution
Answer: 2
Medium
Solve fully. Eight of the ten slots are forced; only the two cells holding 2 and 3 remain interchangeable.
Solved grid — only R2C2 and R3C3 stay undetermined:
| Col 1 | Col 2 | Col 3 | Col 4 | |
|---|---|---|---|---|
| Row 1 | 4 | 6 | 9 | 10 |
| Row 2 | 2 or 3 | 5 | 8 | |
| Row 3 | 3 or 2 | 7 | ||
| Row 4 | 1 |
Fixed slots. 10, 1, then 4 and 6 in Row 1 with 9 (Clues 5, 6), then 5, 7, 8 follow uniquely from the row/column orderings — eight cells fixed.
The undetermined slots. Clue 4 admits 2 and 3 in either of R2C2 / R3C3.