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Rule of Sum and Rule of Product

Seek simple and succinct solutions in these systems by sussing-out the significant symmetries.

Level 3

How many triangles are there in the diagram above?

In the single-elimination NCAA Tournament, 64 teams compete in 6 bracketed rounds. How many games are there in total?

How many 4 -digit positive integers have 2 or more zeroes?

How many parallelograms are formed when a set of 5 parallel lines intersects a set of 4 parallel lines?

Details and Assumptions

  • All parallel lines are extended indefinitely.

How many triangles are there in the above image?


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