Yaksha's questions

Yudhishthira is looking for his brothers in the forest. He finds them near a pond, but all four are dead. "Who can do this to Bhima, Arjuna, Nakula and Sehadeva?" says he. "Yaksha can and I am he," replies a voice. "Why?" says the eldest Pandava. "Because they did not answer my questions and if you do the same, you shall suffer the same fate," Yaksha answers. "Your time begins now, how do you multiply numbers close to 100?"

"That's easy, here's how to use the vedic VERTICALLY AND CROSSWISE method for doing this:

Suppose you want to multiply 88 by 98.

Not easy, you might think, but with

the VERTICALLY AND CROSSWISE method, you can give

the answer immediately.

Both 88 and 98 are close to 100.

88 is 12 below 100 and 98 is 2 below 100.

You can imagine the sum set out like this:

The 86 comes from

subtracting crosswise: 88 - 2 = 86

(or 98 - 12 = 86: you can subtract

either way, you will always get

the same answer).

just 12 x 2: you multiply vertically.

So 88 x 98 = 8624

"This is so easy, it is just mental arithmetic," says Yudhishthira.

"You think that was easy, then show how to multiply numbers just over 100," comes the voice

The eldest Pandava says that consider this:

103 x 104 = 10712

The answer is in two parts: 107 and 12,

107 is just 103 + 4 (or 104 + 3),

and 12 is just 3 x 4.

Similarly 107 x 106 = 11342

107 + 6 = 113 and 7 x 6 = 42

"Wow, ahem ahem, well now tell me a quick way to square numbers that end in 5," Yaksha orders.

"You may use the formula BY ONE MORE THAN THE ONE BEFORE taught in the Vedas," is Yudhishthira's reply.

75² = 5625

75² means 75 x 75.

The answer is in two parts: 56 and 25.

The last part is always 25.

The first part is the first number, 7, multiplied by the number "one more", which is 8:

so 7 x 8 = 56

Similarly 852 = 7225 because 8 x 9 = 72.

"I could have done that, for the lives of one of your four brothers, here's your next question: give me a method for multiplying numbers where the first figures are the same and the last figures add up to 10, ha ha ha," echoes the voice.

Yudhishthira tells the voice to consider the following problem:

32 x 38 = 1216

Both numbers here start with 3 and the last

figures (2 and 8) add up to 10.

Therefore, we just multiply 3 by 4 (the next number up)

to get 12 for the first part of the answer.

We multiply the last figures: 2 x 8 = 16 to

get the last part of the answer.

And 81 x 89 = 7209

We put 09 since we need two figures as in all the other examples.

"Impressive indeed, now the fifth and final question before I allow you to drink water from my pond: how do you multiply a number by 11 quickly," Yaksha shoots.

Yudhishthira does not duck the question, he answers:

To multiply any 2-figure number by 11 we just put

the total of the two figures between the 2 figures.

26 x 11 = 286

Notice that the outer figures in 286 are the 26

being multiplied.

And the middle figure is just 2 and 6 added up.

So 72 x 11 = 792

77 x 11 = 847

This involves a carry figure because 7 + 7 = 14

we get 77 x 11 = 7₁47 = 847.

234 x 11 = 2574

We put the 2 and the 4 at the ends.

We add the first pair 2 + 3 = 5.

and we add the last pair: 3 + 4 = 7.

"Splendid, thanks a lot, you have saved my son from failing the school test," Yaksha says.

"What! You made me do your child's homework, how mean," Yudhishthira says.

"Sorry boss, but I'll make not one, but all your brothers live again for this favour."

"No need, they are rather dumb and keep nagging me for my gambling habit, I wish Shakuni had gambled on my mathematical intellect," says the eldest Pandava and goes his way.

 — Aditya Rishi