Logic Mastery Challenge (Grade 7)
The capstone combines counting, sets, AND/OR, and deduction — a single problem may ask you to count arrangements, then deduce which one fits extra conditions. The skill is choosing the right tool (multiply for the counting principle, eliminate for deduction) and chaining them carefully.
Understanding logic mastery challenge
The capstone combines counting, sets, AND/OR, and deduction — a single problem may ask you to count arrangements, then deduce which one fits extra conditions. The skill is choosing the right tool (multiply for the counting principle, eliminate for deduction) and chaining them carefully.
Key Idea
The capstone combines counting, sets, AND/OR, and deduction — a single problem may ask you to count arrangements, then deduce which one fits extra conditions. The skill is choosing the right tool (multiply for the counting principle, eliminate for deduction) and chaining them carefully.
Seeing it in action
Worked example
From 4 friends, how many ways to pick a pair where one specific friend (Sam) must be included?
Sam is in; choose 1 more from the other 3 → 3 ways. → 3.
Combine counting, sorting, and deduction carefully.
Try a few
Arrange 3 books with the red one first.
the other 2 in 2! ways.
Choose 2 from 5, must include Ana.
1 more from 4.
Even number, 1–10, greater than 4, not a multiple of 4.
6, 10; 8 is a multiple of 4.
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