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.
Understanding logic mastery challenge
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.
Sam pairs with A, B or C: 3 pairs (solid lines). The dashed pairs leave Sam out, so they don’t count. 6 pairs in all, 3 with Sam.
A common mistake, and the fix
Counting every pair instead of only the pairs the condition allows.
4 friends make 6 pairs, but only the pairs that include Sam count: Sam with each of the other 3 friends, so 3 pairs. Apply the condition first, then count what is left.
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.
More logic & counting in Numeris.
Numeris doesn't have a star for logic mastery challenge yet, but its logic & counting constellation practises the skills around it.
Want more practice?
Explore related logic & counting skills in Numeris, browse more free math pages, or join our optional resource updates.
All free math pages →