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Grid Row-Column: Worksheet 10 - Expert Practice Grid Row-Column EXPERT

Ready to master Grid Row-Column? This accuracy focus 👑 worksheet (10/10) presents 20 expert-level challenges. Focus area: application-based learning. Learn to solve grid row-column reasoning tricks, handle fast grid row-column solving, and perfect grid row-column mastery with our step-by-step solutions.

📝 Worksheet 10 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Grid Row-Column
Worksheet 10 of 10 (100% complete)

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 P is at position (1,1) with number 2. • The item at (2,2) has number 12. • The item at (2,2) is Orange colored. • The item with number 8 is in the same column as the Orange 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) = P (Number 2)
- (2,2) = Number 12, Color Orange

2. Column Constraints:
- The number 8 is in the same column as Orange (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 Yellow item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | P | Red | 2 |
| (1,2) | Q | Blue | 8 |
| (1,3) | R | Green | 4 |
| (2,1) | S | Yellow | 6 |
| (2,2) | T | Orange | 12 |
| (2,3) | U | Purple | 10 |

Therefore, the item at (2,2) is T.

Question 2

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 T is at position (1,1) with number 10. • 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 Blue. What item is in Row 2, Column 2?
Step-by-step Solution:

1. Direct Assignments:
- (1,1) = T (Number 10)
- (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 Blue items

4. Diagonal Relationship:
- U is diagonally opposite the Yellow item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | T | Green | 10 |
| (1,2) | S | Orange | 8 |
| (1,3) | U | Red | 6 |
| (2,1) | Q | Yellow | 4 |
| (2,2) | R | Purple | 12 |
| (2,3) | P | Blue | 2 |

Therefore, the item at (2,2) is R.

Question 3

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 T is at position (1,1) with number 2. • The item at (2,2) has number 12. • The item at (2,2) is Yellow colored. • The item with number 8 is in the same column as the Yellow item. • No item in Row 1 is Yellow. What item is in Row 2, Column 2?
Step-by-step Solution:

1. Direct Assignments:
- (1,1) = T (Number 2)
- (2,2) = Number 12, Color Yellow

2. Column Constraints:
- The number 8 is in the same column as Yellow (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 Yellow items

4. Diagonal Relationship:
- S is diagonally opposite the Orange item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | T | Blue | 2 |
| (1,2) | U | Purple | 8 |
| (1,3) | S | Red | 4 |
| (2,1) | P | Orange | 6 |
| (2,2) | R | Yellow | 12 |
| (2,3) | Q | Green | 10 |

Therefore, the item at (2,2) is R.

Question 4

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 Green colored. • The item with number 8 is in the same column as the Green item. • No item in Row 1 is Green. 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 Green

2. Column Constraints:
- The number 8 is in the same column as Green (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 Green items

4. Diagonal Relationship:
- S is diagonally opposite the Blue item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | Q | Orange | 2 |
| (1,2) | R | Purple | 8 |
| (1,3) | S | Yellow | 10 |
| (2,1) | P | Blue | 6 |
| (2,2) | T | Green | 12 |
| (2,3) | U | Red | 4 |

Therefore, the item at (2,2) is T.

Question 5

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 U is at position (1,1) with number 2. • The item at (2,2) has number 12. • The item at (2,2) is Green colored. • The item with number 8 is in the same column as the Green item. • No item in Row 1 is Red. What item is in Row 2, Column 2?
Step-by-step Solution:

1. Direct Assignments:
- (1,1) = U (Number 2)
- (2,2) = Number 12, Color Green

2. Column Constraints:
- The number 8 is in the same column as Green (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 Red items

4. Diagonal Relationship:
- Q is diagonally opposite the Purple item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | U | Yellow | 2 |
| (1,2) | T | Orange | 8 |
| (1,3) | Q | Blue | 10 |
| (2,1) | P | Purple | 6 |
| (2,2) | S | Green | 12 |
| (2,3) | R | Red | 4 |

Therefore, the item at (2,2) is S.

Question 6

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 T is at position (1,1) with number 2. • The item at (2,2) has number 12. • The item at (2,2) is Yellow colored. • The item with number 8 is in the same column as the Yellow item. • No item in Row 1 is Green. What item is in Row 2, Column 2?
Step-by-step Solution:

1. Direct Assignments:
- (1,1) = T (Number 2)
- (2,2) = Number 12, Color Yellow

2. Column Constraints:
- The number 8 is in the same column as Yellow (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 Green items

4. Diagonal Relationship:
- R is diagonally opposite the Green item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | T | Blue | 2 |
| (1,2) | P | Orange | 8 |
| (1,3) | R | Red | 4 |
| (2,1) | U | Green | 6 |
| (2,2) | Q | Yellow | 12 |
| (2,3) | S | Purple | 10 |

Therefore, the item at (2,2) is Q.

Question 7

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 P is at position (1,1) with number 2. • The item at (2,2) has number 12. • The item at (2,2) is Orange colored. • The item with number 8 is in the same column as the Orange 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) = P (Number 2)
- (2,2) = Number 12, Color Orange

2. Column Constraints:
- The number 8 is in the same column as Orange (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 Yellow item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | P | Red | 2 |
| (1,2) | Q | Blue | 8 |
| (1,3) | R | Green | 4 |
| (2,1) | S | Yellow | 6 |
| (2,2) | T | Orange | 12 |
| (2,3) | U | Purple | 10 |

Therefore, the item at (2,2) is T.

Question 8

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 S is at position (1,1) with number 4. • The item at (2,2) has number 12. • The item at (2,2) is Red colored. • The item with number 8 is in the same column as the Red 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) = S (Number 4)
- (2,2) = Number 12, Color Red

2. Column Constraints:
- The number 8 is in the same column as Red (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:
- P is diagonally opposite the Orange item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | S | Yellow | 4 |
| (1,2) | U | Blue | 8 |
| (1,3) | P | Green | 10 |
| (2,1) | Q | Orange | 6 |
| (2,2) | T | Red | 12 |
| (2,3) | R | Purple | 2 |

Therefore, the item at (2,2) is T.

Question 9

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 U is at position (1,1) with number 10. • The item at (2,2) has number 12. • The item at (2,2) is Red colored. • The item with number 8 is in the same column as the Red item. • No item in Row 1 is Red. What item is in Row 2, Column 2?
Step-by-step Solution:

1. Direct Assignments:
- (1,1) = U (Number 10)
- (2,2) = Number 12, Color Red

2. Column Constraints:
- The number 8 is in the same column as Red (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 Red items

4. Diagonal Relationship:
- P is diagonally opposite the Purple item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | U | Green | 10 |
| (1,2) | T | Orange | 8 |
| (1,3) | P | Yellow | 2 |
| (2,1) | S | Purple | 6 |
| (2,2) | Q | Red | 12 |
| (2,3) | R | Blue | 4 |

Therefore, the item at (2,2) is Q.

Question 10

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 S is at position (1,1) with number 6. • The item at (2,2) has number 12. • The item at (2,2) is Orange colored. • The item with number 8 is in the same column as the Orange item. • No item in Row 1 is Red. What item is in Row 2, Column 2?
Step-by-step Solution:

1. Direct Assignments:
- (1,1) = S (Number 6)
- (2,2) = Number 12, Color Orange

2. Column Constraints:
- The number 8 is in the same column as Orange (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 Red items

4. Diagonal Relationship:
- R is diagonally opposite the Yellow item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | S | Blue | 6 |
| (1,2) | Q | Purple | 8 |
| (1,3) | R | Green | 10 |
| (2,1) | T | Yellow | 4 |
| (2,2) | U | Orange | 12 |
| (2,3) | P | Red | 2 |

Therefore, the item at (2,2) is U.

Question 11

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 P is at position (1,1) with number 2. • The item at (2,2) has number 12. • The item at (2,2) is Orange colored. • The item with number 8 is in the same column as the Orange 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) = P (Number 2)
- (2,2) = Number 12, Color Orange

2. Column Constraints:
- The number 8 is in the same column as Orange (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 Yellow item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | P | Red | 2 |
| (1,2) | Q | Blue | 8 |
| (1,3) | R | Green | 4 |
| (2,1) | S | Yellow | 6 |
| (2,2) | T | Orange | 12 |
| (2,3) | U | Purple | 10 |

Therefore, the item at (2,2) is T.

Question 12

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 S is at position (1,1) with number 10. • The item at (2,2) has number 12. • The item at (2,2) is Yellow colored. • The item with number 8 is in the same column as the Yellow item. • No item in Row 1 is Blue. What item is in Row 2, Column 2?
Step-by-step Solution:

1. Direct Assignments:
- (1,1) = S (Number 10)
- (2,2) = Number 12, Color Yellow

2. Column Constraints:
- The number 8 is in the same column as Yellow (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 Blue items

4. Diagonal Relationship:
- R is diagonally opposite the Orange item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | S | Green | 10 |
| (1,2) | T | Purple | 8 |
| (1,3) | R | Red | 6 |
| (2,1) | U | Orange | 4 |
| (2,2) | P | Yellow | 12 |
| (2,3) | Q | Blue | 2 |

Therefore, the item at (2,2) is P.

Question 13

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 S is at position (1,1) with number 2. • The item at (2,2) has number 12. • The item at (2,2) is Orange colored. • The item with number 8 is in the same column as the Orange item. • No item in Row 1 is Red. What item is in Row 2, Column 2?
Step-by-step Solution:

1. Direct Assignments:
- (1,1) = S (Number 2)
- (2,2) = Number 12, Color Orange

2. Column Constraints:
- The number 8 is in the same column as Orange (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 Red items

4. Diagonal Relationship:
- T is diagonally opposite the Red item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | S | Yellow | 2 |
| (1,2) | Q | Blue | 8 |
| (1,3) | T | Purple | 10 |
| (2,1) | U | Red | 6 |
| (2,2) | P | Orange | 12 |
| (2,3) | R | Green | 4 |

Therefore, the item at (2,2) is P.

Question 14

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 10. • The item at (2,2) has number 12. • The item at (2,2) is Blue colored. • The item with number 8 is in the same column as the Blue item. • No item in Row 1 is Yellow. What item is in Row 2, Column 2?
Step-by-step Solution:

1. Direct Assignments:
- (1,1) = Q (Number 10)
- (2,2) = Number 12, Color Blue

2. Column Constraints:
- The number 8 is in the same column as Blue (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 Yellow items

4. Diagonal Relationship:
- S is diagonally opposite the Purple item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | Q | Green | 10 |
| (1,2) | R | Orange | 8 |
| (1,3) | S | Red | 6 |
| (2,1) | T | Purple | 2 |
| (2,2) | P | Blue | 12 |
| (2,3) | U | Yellow | 4 |

Therefore, the item at (2,2) is P.

Question 15

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 S is at position (1,1) with number 2. • The item at (2,2) has number 12. • The item at (2,2) is Blue colored. • The item with number 8 is in the same column as the Blue item. • No item in Row 1 is Blue. What item is in Row 2, Column 2?
Step-by-step Solution:

1. Direct Assignments:
- (1,1) = S (Number 2)
- (2,2) = Number 12, Color Blue

2. Column Constraints:
- The number 8 is in the same column as Blue (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 Blue items

4. Diagonal Relationship:
- P is diagonally opposite the Yellow item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | S | Red | 2 |
| (1,2) | R | Orange | 8 |
| (1,3) | P | Purple | 10 |
| (2,1) | T | Yellow | 6 |
| (2,2) | Q | Blue | 12 |
| (2,3) | U | Green | 4 |

Therefore, the item at (2,2) is Q.

Question 16

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 P is at position (1,1) with number 2. • The item at (2,2) has number 12. • The item at (2,2) is Orange colored. • The item with number 8 is in the same column as the Orange 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) = P (Number 2)
- (2,2) = Number 12, Color Orange

2. Column Constraints:
- The number 8 is in the same column as Orange (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 Yellow item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | P | Red | 2 |
| (1,2) | Q | Blue | 8 |
| (1,3) | R | Green | 4 |
| (2,1) | S | Yellow | 6 |
| (2,2) | T | Orange | 12 |
| (2,3) | U | Purple | 10 |

Therefore, the item at (2,2) is T.

Question 17

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 P is at position (1,1) with number 2. • The item at (2,2) has number 12. • The item at (2,2) is Orange colored. • The item with number 8 is in the same column as the Orange item. • No item in Row 1 is Orange. What item is in Row 2, Column 2?
Step-by-step Solution:

1. Direct Assignments:
- (1,1) = P (Number 2)
- (2,2) = Number 12, Color Orange

2. Column Constraints:
- The number 8 is in the same column as Orange (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 Orange items

4. Diagonal Relationship:
- U is diagonally opposite the Purple item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | P | Blue | 2 |
| (1,2) | R | Red | 8 |
| (1,3) | U | Yellow | 4 |
| (2,1) | S | Purple | 10 |
| (2,2) | T | Orange | 12 |
| (2,3) | Q | Green | 6 |

Therefore, the item at (2,2) is T.

Question 18

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 P is at position (1,1) with number 2. • The item at (2,2) has number 12. • The item at (2,2) is Orange colored. • The item with number 8 is in the same column as the Orange 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) = P (Number 2)
- (2,2) = Number 12, Color Orange

2. Column Constraints:
- The number 8 is in the same column as Orange (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 Yellow item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | P | Red | 2 |
| (1,2) | Q | Blue | 8 |
| (1,3) | R | Green | 4 |
| (2,1) | S | Yellow | 6 |
| (2,2) | T | Orange | 12 |
| (2,3) | U | Purple | 10 |

Therefore, the item at (2,2) is T.

Question 19

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 T is at position (1,1) with number 4. • The item at (2,2) has number 12. • The item at (2,2) is Green colored. • The item with number 8 is in the same column as the Green 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) = T (Number 4)
- (2,2) = Number 12, Color Green

2. Column Constraints:
- The number 8 is in the same column as Green (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:
- Q is diagonally opposite the Blue item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | T | Orange | 4 |
| (1,2) | R | Red | 8 |
| (1,3) | Q | Yellow | 10 |
| (2,1) | S | Blue | 2 |
| (2,2) | U | Green | 12 |
| (2,3) | P | Purple | 6 |

Therefore, the item at (2,2) is U.

Question 20

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 P is at position (1,1) with number 2. • The item at (2,2) has number 12. • The item at (2,2) is Orange colored. • The item with number 8 is in the same column as the Orange 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) = P (Number 2)
- (2,2) = Number 12, Color Orange

2. Column Constraints:
- The number 8 is in the same column as Orange (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 Yellow item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | P | Red | 2 |
| (1,2) | Q | Blue | 8 |
| (1,3) | R | Green | 4 |
| (2,1) | S | Yellow | 6 |
| (2,2) | T | Orange | 12 |
| (2,3) | U | Purple | 10 |

Therefore, the item at (2,2) is T.
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