Multiplying by 11 Ekādhikena Pūrveṇa
Write the outer digits, then slot in the sum of every pair of neighbours. Carries ripple left, exactly like column addition — but there's nothing to carry through.
Squaring numbers ending in 5 Antyayor Daśake'pi
Drop the 5. Multiply what's left by "one more than itself." Stick 25 on the end. Done — no long multiplication required.
Nikhilam multiplication Nikhilaṁ Navataścaramaṁ Daśataḥ
Works best when both numbers hug a round base like 100 or 1000. Measure each number's distance from the base, cross-add for the left half, multiply the distances for the right half.
Criss-cross multiplication Ūrdhva-Tiryagbhyām
Any two 2-digit numbers, three diagonal sweeps, no partial-products written out. Units straight down, tens crossed, hundreds straight down.
Instant subtraction from a base Sarvataḥ / Sarvaṁ Daśataḥ
Subtracting from 100, 1000, or any round number? Take every digit from 9, except the last one — take that from 10. No borrowing, ever.