# Impressing Your Vietnamese Friends with Mental Arithmetic

During my travels I spent a week in Ho Chi Minh City, absolutely loving my time there! One day, after visits to museums, temples and little shops, I ended up in a comfortable bubble tea store. While sipping my passion fruit bubble tea, a group of Vietnamese university students came in and started practicing their English. After some time, they asked whether I could help them with their English and I joined their study group. During introductions, I mentioned that I was a mathematician. Immediately I was bombarded by mental arithmetic questions and had to prove my worth. With the help of something I’d read about ages ago and never forgotten, I managed to impress them.

There is an ancient Indian form of mathematics known as **Vedic mathematics**. (Admittedly, there is some controversy surrounding it.) This type of mathematics involves a **ton of tricks** for **mental arithmetic**.

One of my all-time favorite tricks, and the one that came in handy, is a quick way for multiplying two-digit numbers with the *same first digit* and whose *second digits add up to 10*. (For example 63·67.)

**Method**:

- Perform the following multiplication: (
*first digit*)·(*first digit*+1). The result will form the**first few digits**of the number. - Then do: (
*second digit of 1*)·(^{st}number*second digit of 2*). This yields the^{nd}number**last two digits**of the result.

Note: If you perform 1·9=9, then write 09, as we need the product to take up the last*two*digits of the answer. - Write the results next to one another and you end up with the answer.

**Example**: Let us take a look at 63·67:

- The first digit of 63 and 67 is 6. Hence we do 6·(6+1)=6·7=42.
- The second digits of 63 and 67 are 3 and 7 respectively. We do 3·7=21.
- Putting these answers together gives 4221.

If, after performing the calculations on the right hand side, we were forced to express *100a*(*a+1*)*+b*(*10-b*) in words, we would get:

*x·y*=the product of (*first digit of x & y) *and ((*first digit of x & y) + 1*), followed by the two digits given by the product of (*last digit of x*) and (*last digit of y*)

This is exactly what our method states.

Let me know about **your** favorite number tricks!