Tens Match

Technique: Same tens, units summing to 10

When two 2-digit numbers share the same tens digit and their units digits add to 10, the product is a one-step pattern: tens × (tens+1) | units × units, where the right-hand block is always two digits (pad with a leading zero if needed).

Examples

• 83 × 87 → 8×9 = 72, units 3×7 = 21 → 7221
• 41 × 49 → 4×5 = 20, units 1×9 = 09 → 2009
• 24 × 26 → 2×3 = 6, units 4×6 = 24 → 624
• 62 × 68 → 6×7 = 42, units 2×8 = 16 → 4216

Why does this work?

If the factors are (10t + u) and (10t + (10−u)), the algebra collapses: the cross-terms add to 10t × 10 = 100t, which lifts the leading t×t into t×(t+1). The remaining u×(10−u) sits in the bottom two digits.

Pad the right block to two digits — 1×9 = 09, not 9.

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