Sub-Sūtra 6 of 13

Antyayoḥ Daśake'pi

When the final digits add to 10

Multiplication when last digits sum to 10 and other digits are equal.

When to use

Numbers like 43 × 47, 62 × 68.

How it works

Left part: the common digit × (common digit + 1). Right part: product of last digits (pad to 2 digits).

Memory formula

Same tens and unit digits sum to 10: tens × next tens | units product.

Worked examples

Problem 1

43 × 47

0/4

Try it yourself

Try to solve, then reveal the steps one at a time.

easy

Compute 62 × 68

medium

Compute 81 × 89

Code in your favourite language

Same tens, units summing to 10: tens × (tens+1) | units × units.

Python

def antyayoh(a: int, b: int) -> int:
    t = a // 10
    u1, u2 = a % 10, b % 10
    assert a // 10 == b // 10 and u1 + u2 == 10
    return (t * (t + 1)) * 100 + u1 * u2

print(antyayoh(62, 68))  # 4216

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