Power Multiply

Technique: Multiply numbers near 100

Both numbers below 100

Step 1: Find each number's deficit from 100.

Step 2: Cross-subtract: take either number minus the other's deficit → first two digits.

Step 3: Multiply the deficits → last two digits (pad with 0 if single digit).

• 97 × 96 → deficits 3, 4. First: 97−4 = 93. Last: 3×4 = 12. Answer: 9312
• 93 × 98 → deficits 7, 2. First: 93−2 = 91. Last: 7×2 = 14. Answer: 9114
• 88 × 96 → deficits 12, 4. First: 88−4 = 84. Last: 12×4 = 48. Answer: 8448

Both numbers above 100

Same idea but cross-add the surpluses:

• 103 × 104 → surpluses 3, 4. First: 103+4 = 107. Last: 3×4 = 12. Answer: 10712
• 108 × 106 → surpluses 8, 6. First: 108+6 = 114. Last: 8×6 = 48. Answer: 11448

Why does this work?

For a, b near 100: a×b = (a−(100−b))×100 + (100−a)(100−b). The base-100 trick generalises to any round number.

Every question has a 30 second shot clock.