# Finding the unknown digits

What is the sum of the digits a and b if the multiplication 3a7 x 52b = 181,481?

This is a question given to the intermediate group in the 3rd MATH-Inic Vedic Mathematics National Challenge held last April 10, 2023.

Only about 1/3 of the more than 700 participants in that group were able to get the correct answer.

A powerful combination of two Vedic Math sutras or word formulae – the First by the First and the Last  by the Last (FFLL) and the Product of the Sums is the Sum of the Product (PSSP) – can be used to quickly determine the answer.

The product of the last digits of the multiplicands (the Last by the Last), 7 and b ends in 1; so, b must be 3 and 52b must be 523. Its digit sum is 1 ( 5 + 2 + 3 = 10 and 1 + 0 = 1).

The digit sum of the product 181,481, by casting out 1 & 8 and 8 & 1, is 5 ( 1+ 4).

Using PSSP, we have the digit sum of 3a7 x 1 = 5.  Therefore the digit sum of 3a7 is 5. Since 3 + 7 = 10 and 1+ 0 = 1, then 1 + a = 5 and a = 4.

(a + b) is (4 + 3) or 7.

More examples on the use of FFLL and PSSP in arithmetic calculations can be found in chapters 2 and 3  of our book, Algebra Made Easy as Arithmetic (AMEA) while their applications in checking algebraic computations are discussed in chapters 20 and 21.

AMEA can be purchased for only P300 thru our MATH-Inic Philippines FB page, https://www.facebook.com/MATHInicPhils.