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Number and algebra puzzles (contest style)
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Learn it Look for shortcuts: $x^2 - y^2 = (x + y)(x - y)$; sums of sequences = average × count; new operations just mean "follow the rule".
Example: If x + y = 12 and x − y = 3, find $x^2 - y^2$.
- $x^2 - y^2 = (x + y)(x - y)$.
- $= 12 \times 3$.
- $= 36$, without finding x or y.
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