The eight tricks
- Times 5 (68 × 5 = 340): Halve the number, then times 10.
- Times 11 (43 × 11 = 473): Write the two digits apart, and put their sum in the middle.
- Take from 1000 (1000 − 357 = 643): Take every digit from 9, and the last digit from 10. From the sutra Nikhilam Navatashcaramam Dashatah, “All from 9 and the last from 10”.
- Squares ending in 5 (35² = 1225): Multiply the front by one more than itself, then write 25. From the sutra Ekadhikena Purvena, “By one more than the one before”.
- Times 9, 99, 999 (47 × 99 = 4653): Write one less than the number, then each of its digits taken from 9. From the sutra Ekanyunena Purvena, “By one less than the one before”.
- Last digits make 10 (43 × 47 = 2021): Front times one more, then the last digits multiplied (as two digits). From the sutra Antyayor Dashake'pi, “When the last digits add up to 10”.
- Close to 100 (97 × 96 = 9312): Cross-subtract the gaps from 100, then multiply the gaps (as two digits). From the sutra Nikhilam Navatashcaramam Dashatah, “All from 9 and the last from 10”.
- Vertically and crosswise (23 × 41 = 943): Left digits multiplied, then the two cross products added, then right digits multiplied. Carry from the right. From the sutra Urdhva Tiryagbhyam, “Vertically and crosswise”.
How it works here
Each trick starts with one worked example, written out a step at a time, with the same colour for the same piece in every step. Then you get 10 questions to do in your head. Early questions are gentle and later ones stretch the trick (bigger numbers, a carry, numbers over 100). If you get one wrong you see the trick worked out for that exact question.
Stars count the answers you got on your own: 10 for three stars, 8 for two, 5 for one. Once two tricks have a star, the Mixed round opens, where part of the challenge is spotting which trick fits.
Where “Vedic maths” comes from
The name comes from the book Vedic Mathematics by Bharati Krishna Tirtha, published in 1965, five years after he died. It lists 16 short sutras (rules) and 13 sub-sutras. He said they came from the Vedas, but historians of mathematics have pointed out that they aren't found in the known Vedic texts, so the tricks are best seen as his own clever collection. (More on Wikipedia.)
Either way, the tricks are real and they work, and every one of them is ordinary algebra in disguise. Open “Why it works” under any lesson to see it.