Question 1
Six items (P, Q, R, S, T, U) are arranged in a 2×3 grid (2 rows, 3 columns). Each has a unique color and associated number.
Colors: Red, Blue, Green, Yellow, Orange, Purple
Numbers: 2, 4, 6, 8, 10, 12
Given information:
• Item Q is at position (1,1) with number 2.
• The item at (2,2) has number 12.
• The item at (2,2) is Purple colored.
• The item with number 8 is in the same column as the Purple item.
• No item in Row 1 is Purple.
What item is in Row 2, Column 2?
Step-by-step Solution:
1. Direct Assignments:
- (1,1) = Q (Number 2)
- (2,2) = Number 12, Color Purple
2. Column Constraints:
- The number 8 is in the same column as Purple (Column 2)
- Therefore, either (1,2) or (2,2) has number 8
- Since (2,2) has 12, (1,2) must have number 8
3. Row Constraints:
- Row 1 has no Purple items
4. Diagonal Relationship:
- R is diagonally opposite the Orange item
Final Grid:
| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | Q | Yellow | 2 |
| (1,2) | T | Red | 8 |
| (1,3) | R | Blue | 10 |
| (2,1) | S | Orange | 4 |
| (2,2) | P | Purple | 12 |
| (2,3) | U | Green | 6 |
Therefore, the item at (2,2) is P.
1. Direct Assignments:
- (1,1) = Q (Number 2)
- (2,2) = Number 12, Color Purple
2. Column Constraints:
- The number 8 is in the same column as Purple (Column 2)
- Therefore, either (1,2) or (2,2) has number 8
- Since (2,2) has 12, (1,2) must have number 8
3. Row Constraints:
- Row 1 has no Purple items
4. Diagonal Relationship:
- R is diagonally opposite the Orange item
Final Grid:
| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | Q | Yellow | 2 |
| (1,2) | T | Red | 8 |
| (1,3) | R | Blue | 10 |
| (2,1) | S | Orange | 4 |
| (2,2) | P | Purple | 12 |
| (2,3) | U | Green | 6 |
Therefore, the item at (2,2) is P.