could you please help me make a logic puzzle with the following guidelines to successfully complete the puzzle:

• Your puzzle must involve the principle of inclusion and exclusion and must have a minimum of seven clues to help solve the puzzle.
• Ensure that your puzzle is solvable by having a classmate or other appropriate partner try to solve it.
• While you observe your partner solving the puzzle, record the strategies used in the puzzle solution.
• After your partner has solved the puzzle, discuss which clues worked well and which clues may need a bit of improvement. Make these revisions to your puzzle.

You must include the following elements in your puzzle:

clear and concise clues to your puzzle

a detailed solution to your puzzle, which should include all diagrams, charts, formulas, algebraic steps, and a description of the logic used in solving the puzzle

References:

Here is an example of a puzzle:

Communicates Understanding to Others Graphs, Diagrams, Demonstrates an Charts, andlor Understanding of Demonstrates Reasoning Skills Criteria Standards Models the Concept Demonstrates reasoning by making Graphs, diagrams. charts, and/or models Responses to questions are insightful Uses specific mathematical are accurate and and reect a in-depth analysis of language to explain demonstrate the comprehensive strategies and draws understanding and student's understanding of the insightful conclusions. provides understanding. mathematical in-depth support for concepts. conclusions. EXAMPLE 1 Solving a puzzle using the Principle of Exclusion and Inclusion Use the following clues to answer the questions below: - 28 children have a dog, a cat, or a bird. - 13 children have a dog. ' 13 children have a cat. ' 13 children have a bird. ' 4 children have a dog and a cat. ' 3 children have a dog and a bird. - 2 children have a cat and a bird. 0 No child has two of each type of pet. a) How many children have a cat, a dog, and a bird? b) How many children have only one pet? Hailey's Solution: Using the Principle of Inclusion and Exclusion a) P = {children with pets} C = {children with a cat} I defined the sets in this situation. B = {children with a bird} D = {children with a dog} Let x represent the number of children with a bird, I defined the variable x. a cat, and a dog. I drew a Venn diagram to show how the numbers of elements in the four sets were related. n(B) + n(C) + n(D) - n(BN C) - n(BND) - n(CN D) + n(Bn CND) = n(BU CUD) Each circle overlaps the other two circles. I determined the sum of the three circles using the Principle of Inclusion and Exclusion to deal with the overlapping areas. 13 + 13 + 13 - (x + 2) - (x + 3) - (x + 4) + x=28 I knew that each circle represents 39 - x-2 -x- 3-x- 4+x=28 13 children, and there are 28 children 30 - 2x = 28 in total. I solved for x. -2x = -2 x = 1 One child has three different types of pets. The area of the Venn diagram where all three circles overlap represents children who have all three pets. I revised my diagram. b) Children with one pet = Total number of children - Children who have more than one pet Children with one pet = 28 - (1 + 2 + 3 + 4) I subtracted the number of children Children with one pet = 28 - 10 who have more than one pet from Children with one pet = 18 the total number of children. Therefore, 18 children have only one type of pet. NEL 1.4 Applications of Set Theory 41