Photo AI
Noughts and Crosses is a two-person game played on a 3 × 3 grid, made up of 9 small squares - Junior Cycle Mathematics - Question 3 - 2015
Question 3
Noughts and Crosses is a two-person game played on a 3 × 3 grid, made up of 9 small squares. We call each of the 3 rows, 3 columns, and 2 diagonals a line. An exampl... show full transcript
Worked Solution & Example Answer:Noughts and Crosses is a two-person game played on a 3 × 3 grid, made up of 9 small squares - Junior Cycle Mathematics - Question 3 - 2015
Step 1
In the 3 × 3 grid below, write in each small square the number of different lines to which it belongs.
Answer
In a 3 × 3 grid, each small square belongs to the following lines:
3 3 2
2 2 2
3 2 3
- Each cell in the corners belongs to 3 lines (1 row, 1 column, and 1 diagonal).
- Each edge cell belongs to 2 lines (1 row and 1 column).
- The center cell belongs to 4 lines (2 diagonals, 1 row, and 1 column).
Step 2
Step 3
For certain values of n, the maximum number of different lines to which a small square can belong is 4, while for other values of n this maximum number is 3. State for which values of n this maximum number is 4, and for which values of n this maximum number is 3. Justify your answer.
Answer
The maximum number of lines is 4 when n is odd (for example, n = 3, 5, 7...); this is because the center square will align with both diagonals. For even n (n = 4, 6, 8...), any central square won't belong to both diagonals, resulting in a maximum of 3 lines.