Creating a Tromino with n=8 and Missing Square at (4,6)

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In summary, the goal is to create a tromino with n=8, where the missing square is located four squares from the left and six squares from the top. The input is the value of n and the location of the missing square, and the output is a tiling of an n x n deficient board. The object being created is a polyomino consisting of three squares, and n refers to the number of squares in the object.
  • #1
Bucs44
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I'm trying to create a tromino where n=8 and the missing square is four from the left and six from the top.

Here's what I have so far:

Input: n, a power of 8; and the location L of the missing square
Output: A tiling of an n x n deficient board
1. tile(n,L) {
2. if (n==8) {


I'm unsure of how to denote where the missing square is. Can anyone help?
 
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What's a tromino?
 
  • #3
StatusX said:
What's a tromino?

That doesn't bode well for me - but a tromino is an object made up of three squares. It can also be called a polyomino.
 
  • #4
Well, that doesn't really narrow it down. But I can guess what you mean is one of the two 2D shapes consisting of 3 squares, where each shares a side with one of the others, ie, they're in a straight line or they make an L.

But then what does n refer to? Or do you mean for there to be n squares, where n isn't necessarily 3? (I'm betting this is actually what "polyomino" refers to)
 
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1. How do you create a tromino with n=8 and a missing square at (4,6)?

To create a tromino with n=8 and a missing square at (4,6), you will need to first draw a grid with 8 rows and 8 columns. Then, place a missing square at the coordinates (4,6) by leaving that square blank. Next, you will need to divide the remaining 63 squares into 21 groups of three squares each. Each group of three squares represents one tromino. Finally, arrange the 21 trominos on the grid in such a way that they cover all of the squares except for the missing square at (4,6).

2. What is the significance of the missing square in a tromino with n=8?

The missing square in a tromino with n=8 represents a unique challenge in creating the tromino. With n=8, there are an odd number of squares in the grid, which means that it is impossible to cover all of the squares with an equal number of trominos. Therefore, one square will always be left blank, and its position will determine the shape and orientation of the tromino.

3. Can a tromino with n=8 and a missing square at (4,6) have rotational symmetry?

No, a tromino with n=8 and a missing square at (4,6) cannot have rotational symmetry. In order for a shape to have rotational symmetry, it must be able to rotate 180 degrees without changing its appearance. However, in a tromino with n=8 and a missing square at (4,6), the missing square will always be in a different position after a 180 degree rotation, thus breaking any potential rotational symmetry.

4. How many different arrangements of trominos with n=8 and a missing square at (4,6) are possible?

There are actually 4,896 different arrangements of trominos with n=8 and a missing square at (4,6) that are possible. This is due to the unique challenge of the missing square and the fact that there are 21 different ways to arrange the 21 trominos on the grid.

5. Can a tromino with n=8 and a missing square at (4,6) have reflectional symmetry?

Yes, a tromino with n=8 and a missing square at (4,6) can have reflectional symmetry. Reflectional symmetry means that a shape can be reflected over a line and still maintain its appearance. In a tromino with n=8 and a missing square at (4,6), if the missing square is placed on a line of symmetry, then the tromino can have reflectional symmetry. However, this is not always the case, as the missing square can also break any potential reflectional symmetry.

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