make a 5 by 5 tile uisng 5 different colors. None can be in the same row nor be diagional.
let g=green; b=blue; r=red; y=yellow; o=orange
This is one example
g,b,r,y,o
r,y,o,g,b
o,g,b,r,y
b,r,y,o,g
y,o,g,b,r
Notice that the order is the same in each line, shifted by 2
To create a 5 by 5 tile using 5 different colors where no colors can be in the same row or diagonal, you can follow these steps:
1. Determine the number of color combinations: Since you have 5 different colors, you have a total of 5! (5 factorial) which is equal to 120 possible permutations.
2. Start with an empty 5 by 5 tile.
3. Assign a color from the 5 available choices to the first row (5 choices).
4. Move to the second row and assign a color that is different from the one used in the first row. You have 4 choices left.
5. Continue this process for the remaining rows, ensuring that no color is repeated in the same row or any diagonal.
6. Repeat steps 3-5 for each of the remaining rows, always considering the colors used in the previous rows to avoid repetition.
Here's an example of how you could assign colors to each tile:
1st row: Blue, Green, Purple, Orange, Red
2nd row: Green, Purple, Orange, Red, Blue
3rd row: Purple, Orange, Red, Blue, Green
4th row: Orange, Red, Blue, Green, Purple
5th row: Red, Blue, Green, Purple, Orange
By following these steps, you will have a 5 by 5 tile with 5 different colors, where no color is in the same row or diagonal.