Question

below are 12 pentominoes with corresponding letter codes. your task is to create a set of 4 yes - or - no questions that uniquely classify each pentomino. uniquely classifying means that no 2 letters have exactly the same answers to all 4 questions. are the numbers that are present above a vowel? longest segment of tiles do they all have a connection of 3?

Explanation:

To create 4 yes - no questions to uniquely identify each pentomino, we can use the following approach:

Question 1: Does the pentomino have a vertical line of 4 or more squares?

• For example, the pentomino labeled 'I' has a horizontal line of 5 squares (which can be considered a vertical line of 5 if rotated), and the pentomino labeled 'L' (the tall one) has a vertical line of 4 squares. Pentominoes like 'F', 'M', 'N', 'P', 'T', 'U', 'V', 'X', 'Y', 'Z' do not have a vertical line of 4 or more squares.

Question 2: Is the pentomino symmetric about a vertical axis?

• The pentomino 'U' is symmetric about a vertical axis, and the pentomino 'X' is symmetric about both vertical and horizontal axes. Pentominoes like 'F', 'I', 'L', 'M', 'N', 'P', 'T', 'V', 'Y', 'Z' do not have vertical symmetry (or have different types of symmetry).

Question 3: Does the pentomino contain a 2x2 square of squares?

• The pentomino 'P' contains a 2x2 square (with an extra square attached), and the pentomino 'U' also has a sort of 2x2 - like structure at the bottom. Pentominoes like 'F', 'I', 'L', 'M', 'N', 'T', 'V', 'X', 'Y', 'Z' do not contain a 2x2 square of squares.

Question 4: Does the pentomino have a "cross" - like shape (with a central square and squares attached to all four sides)?

• Only the pentomino 'X' has a cross - like shape with a central square and squares attached to the top, bottom, left, and right.

By answering these four yes - no questions, we can uniquely identify each of the 12 pentominoes, as no two pentominoes will have the same set of answers to all four questions.

If we were to analyze a specific pentomino, say 'X':

• Answer to Question 1: No (it does not have a vertical line of 4 or more squares in the traditional sense of a long vertical strip)
• Answer to Question 2: Yes (it is symmetric about a vertical axis)
• Answer to Question 3: No (it does not contain a 2x2 square)
• Answer to Question 4: Yes (it has a cross - like shape)

For the pentomino 'I':

• Answer to Question 1: Yes (it has a long horizontal/vertical line of 5 squares)
• Answer to Question 2: Yes (it is symmetric about both vertical and horizontal axes)
• Answer to Question 3: No (it is a straight line, no 2x2 square)
• Answer to Question 4: No (it is a straight line, not a cross)

These questions can be used to distinguish between the different pentomino shapes based on their geometric properties.

Answer:

To create 4 yes - no questions to uniquely identify each pentomino, we can use the following approach:

Question 1: Does the pentomino have a vertical line of 4 or more squares?

• For example, the pentomino labeled 'I' has a horizontal line of 5 squares (which can be considered a vertical line of 5 if rotated), and the pentomino labeled 'L' (the tall one) has a vertical line of 4 squares. Pentominoes like 'F', 'M', 'N', 'P', 'T', 'U', 'V', 'X', 'Y', 'Z' do not have a vertical line of 4 or more squares.

Question 2: Is the pentomino symmetric about a vertical axis?

• The pentomino 'U' is symmetric about a vertical axis, and the pentomino 'X' is symmetric about both vertical and horizontal axes. Pentominoes like 'F', 'I', 'L', 'M', 'N', 'P', 'T', 'V', 'Y', 'Z' do not have vertical symmetry (or have different types of symmetry).

Question 3: Does the pentomino contain a 2x2 square of squares?

• The pentomino 'P' contains a 2x2 square (with an extra square attached), and the pentomino 'U' also has a sort of 2x2 - like structure at the bottom. Pentominoes like 'F', 'I', 'L', 'M', 'N', 'T', 'V', 'X', 'Y', 'Z' do not contain a 2x2 square of squares.

Question 4: Does the pentomino have a "cross" - like shape (with a central square and squares attached to all four sides)?

• Only the pentomino 'X' has a cross - like shape with a central square and squares attached to the top, bottom, left, and right.

By answering these four yes - no questions, we can uniquely identify each of the 12 pentominoes, as no two pentominoes will have the same set of answers to all four questions.

If we were to analyze a specific pentomino, say 'X':

• Answer to Question 1: No (it does not have a vertical line of 4 or more squares in the traditional sense of a long vertical strip)
• Answer to Question 2: Yes (it is symmetric about a vertical axis)
• Answer to Question 3: No (it does not contain a 2x2 square)
• Answer to Question 4: Yes (it has a cross - like shape)

For the pentomino 'I':

• Answer to Question 1: Yes (it has a long horizontal/vertical line of 5 squares)
• Answer to Question 2: Yes (it is symmetric about both vertical and horizontal axes)
• Answer to Question 3: No (it is a straight line, no 2x2 square)
• Answer to Question 4: No (it is a straight line, not a cross)

These questions can be used to distinguish between the different pentomino shapes based on their geometric properties.