Multiply Two 2-Digit Numbers Ending in Same Digit

Problem

Multiplying numbers like 23×27 or 41×49 requires full multiplication.

Solution

When tens digit is same and ones add to 10: Multiply tens×(tens+1), then ones×ones.

Benefit

Special case shortcut that saves 80% of calculation time.

Example

23 × 27 (same tens 2, ones add to 10: 3+7=10):
Tens: 2 × (2+1) = 2 × 3 = 6
Ones: 3 × 7 = 21
Answer: 621

41 × 49:
Tens: 4 × 5 = 20
Ones: 1 × 9 = 09
Answer: 2009