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Browse all 16 sutras. Arithmetic sutras use generated drills; algebra and concept sutras use curated proof-style prompts.
एकाधिकेन पूर्वेण
Ekadhikena Pūrveṇa
When the last digit is 5, the prefix does all the work — multiply it by itself plus one.
निखिलं नवतश्चरमं दशतः
Nikhilaṃ Navataścaramaṃ Daśataḥ
Find how far each number is from the nearest power of 10. Those distances do the multiplication for you.
ऊर्ध्व-तिर्यग्भ्याम्
Ūrdhva-Tiryagbhyāṃ
Multiply digits vertically, then crosswise, then vertically again — the pattern forms an expanding diamond.
परावर्त्य योजयेत्
Parāvartya Yojayet
Division by a near-10 divisor: transpose the sub-digits of the divisor (negate them) and use them as a flag that helps you divide step by step.
शून्यं साम्यसमुच्चये
Śūnyaṃ Sāmyasamuccaye
If the same expression appears on both sides of an equation with equal sums, it equals zero — the equation solves instantly.
आनुरूप्ये शून्यमन्यत्
Ānurūpye Śūnyamanyat
In simultaneous equations, if the ratio of coefficients matches, one variable vanishes and the other solves directly.
संकलन-व्यवकलनाभ्याम्
Saṅkalana-vyavakalanābhyāṃ
Add the two equations to get one answer; subtract them to get another. Two equations → two answers in two steps.
पूरणापूरणाभ्याम्
Pūraṇāpūraṇābhyāṃ
Complete the square (or cube) by adding and subtracting the missing term — Vedic style completion method.
चलन-कलनाभ्याम्
Calanā-Kalanābhyāṃ
Use calculus-like derivative thinking: find roots of a polynomial by examining its rate of change pattern.
यावदूनम्
Yāvadūnaṃ
Square a number near a base: subtract (or add) the deficiency to get the left part, square the deficiency for the right part.
व्यष्टिसमष्टि
Vyaṣṭisamaṣṭhi
Factor a quadratic by finding two numbers whose sum is the middle coefficient and product is the last — the Vedic way to factor trinomials.
शेषाण्यङ्केन चरमेण
Śeṣāṇyaṅkena Caramaṇa
Express numbers in terms of a reference base and use remainders (vinculum) to simplify complex calculations.
सोपान्त्यद्वयमन्त्यम्
Sopāntyadvayamantyam
In certain sum-of-fractions equations, the answer combines the last and second-to-last terms in a specific ratio.
एकन्यूनेन पूर्वेण
Ekanyūnena Pūrveṇa
Multiply by a string of 9s: subtract 1 from the multiplicand for the left part; find the complement of the multiplicand for the right part.
गुणितसमुच्चयः
Guṇitasamuccayaḥ
The digit sum of a product equals the digit sum of the product of the individual digit sums — a verification tool.
गुणकसमुच्चयः
Guṇakasamuccayaḥ
The factors of an expression when evaluated at a value equal the expression's value — use this to verify factorizations.