A gym has 9 lockers arranged in a 3×3 grid (3 rows, 3 columns). Each locker has a unique numeric code from 1 to 9 (each of the numbers 1 to 9 is used exactly once, one per locker). The following facts are known about the arrangement:
1. The code in the centre locker (row 2, column 2) is 6.
2. The sum of the codes in row 1 (the top row) is 18.
3. The code 8 is in the bottom-left locker, and code 5 is in the bottom-right locker.
4. The sum of the codes in column 3 (the rightmost column) is 15.
5. The locker with code 4 is immediately to the left of the locker with code 6 (i.e., in the same row, one column before it).
6. The locker with code 1 is immediately below the locker with code 9 (i.e., in the same column, one row below it).
7. The code in the top-left locker is greater than 5.
1. The code in the centre locker (row 2, column 2) is 6.
2. The sum of the codes in row 1 (the top row) is 18.
3. The code 8 is in the bottom-left locker, and code 5 is in the bottom-right locker.
4. The sum of the codes in column 3 (the rightmost column) is 15.
5. The locker with code 4 is immediately to the left of the locker with code 6 (i.e., in the same row, one column before it).
6. The locker with code 1 is immediately below the locker with code 9 (i.e., in the same column, one row below it).
7. The code in the top-left locker is greater than 5.
Question 1
Numerical answer
What is the code of the top-left locker (row 1, column 1)?
Show answer and solution
Answer: 7
From clue 5, 4 is immediately left of 6, and clue 1 says 6 is in the centre (row2,col2), so 4 is in row2,col1. From clue 6, 1 is directly below 9; testing positions consistent with the other clues places 9 in row1,col3 and 1 in row2,col3, which (with clue 4: column-3 sum=15) forces the third row-2 cell... Working through all clues (verified by exhaustive check) gives the unique grid: Row1 = 7,2,9; Row2 = 4,6,1; Row3 = 8,3,5. Clue 7 (top-left > 5) confirms it is 7, not 2.
Question 2
Single correct option
What is the code of the top-middle locker (row 1, column 2)?
- A. 1
- B. 2
- C. 3
- D. 9
Show answer and solution
Answer: (B) 2
Using the unique solved grid — Row1: 7,2,9; Row2: 4,6,1; Row3: 8,3,5 — the top-middle locker (row1,col2) has code 2.
Question 3
Numerical answer
What is the sum of the codes in row 2 (the middle row)?
Show answer and solution
Answer: 11
Row 2 of the solved grid is 4, 6, 1 (left to right). Sum = 4+6+1 = 11.
Question 4
Single correct option
Which locker (by position) contains the code 9?
- A. Top-left
- B. Top-right
- C. Middle-right
- D. Bottom-middle
Show answer and solution
Answer: (B) Top-right
From the solved grid, Row1 = 7,2,9, so code 9 is in row1,col3 — the top-right locker. This is consistent with clue 6, since code 1 (directly below 9) is at row2,col3.
Question 5
Numerical answer
What is the sum of the codes on the main diagonal (top-left, centre, bottom-right lockers)?
Show answer and solution
Answer: 18
Main diagonal = top-left (7) + centre (6) + bottom-right (5) = 7+6+5 = 18.
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