# Finding the unknown digits

What is the sum of the digits **a** and **b** if the multiplication 3**a**7 x 52**b** = 181,481?

This is a question given to the intermediate group in the 3^{rd} 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.