Question

The Colored Grid

Color the grid below to meet the following conditions
4 squares should be colored blue
• 3 squares should be colored red
.
3 squares should be colored white
.
3 squares should be colored green
• 3 squares should be colored yellow
no square of the same color appears more than once in any horizontal, vertical, or
diagonal line.
How can the grid be colored?

Answer 1

To meet the given conditions on a 5x5 grid, color 4 squares blue, 3 red, 3 white, 3 green, and 3 yellow. Ensure no color repeats in any horizontal, vertical, or diagonal line, creating a diverse and balanced arrangement.

A possible coloring scheme for the 5x5 grid to meet the given conditions:

1. **Blue Squares (4):** Randomly place four blue squares on the grid, ensuring they don't share the same row, column, or diagonal.

2. **Red Squares (3):** Place three red squares on the grid, following the same rule as above.

3. **White Squares (3):** Place three white squares on the grid, following the same rule.

4. **Green Squares (3):** Place three green squares on the grid, following the rule.

5. **Yellow Squares (3):** Place three yellow squares on the grid, following the rule.

Ensure that each color is used exactly the specified number of times, and no two squares of the same color appear in the same row, column, or diagonal. The arrangement can vary, but the key is to maintain the specified color count and avoid repetitions in each line.