The problem involves arranging tiles for the letters of the alphabet on a classroom wall, following specific rules. Let's break this down:

• The alphabet has 26 letters.
• The tiles must form a rectangle.
• The rectangle must have 6 rows.
• The rectangle must have the fewest possible columns.

To determine the number of columns:

1. We need to find the smallest multiple of 6 that is greater than or equal to 26 (since there are 26 letters).

   The smallest multiple of 6 greater than 26 is 30, because $6 \times 5 = 30$.

2. The rectangle will contain 30 tiles (letters + blanks), arranged into 6 rows.

3. To find the number of columns, we divide 30 by 6: $\frac{30}{6} = 5$

So, there will be 5 columns of tiles.

Would you like more details or have any questions? Here are some related questions to think about:

1. How many blank tiles will be in the arrangement?
2. What would happen if there were more than 26 letters?
3. Can you think of another shape for the rectangle with 6 rows that still satisfies the conditions?
4. What if the rectangle had 5 rows instead of 6?
5. How would the arrangement change if there were 50 letters instead of 26?

Tip: Always check if a division produces an integer to confirm proper arrangement of rows and columns.