A perplexing math puzzle is doing the rounds online, intriguing people with the claim that only geniuses are able to solve it.
On the face of it, the puzzle looks simple: If 11 × 11 = 4, and 22 × 22 = 16, then what is 33 × 33 = ? People are engaged in heated debate over the true answer, so before reading ahead, try it for yourself; what do you think the answer could be?
Let’s expand upon two interpretations, which incidentally represent the two ways that thousands of people believe are the best ways to solve this interesting conundrum.
Answer 1: 33 × 33 = 36
This method is called the “product of the sum of the digits,” and it’s easier to break down than its name might suggest.It involves adding the digits on either side of the multiplication signs on the left side of each equation, which when multiplied together should equal the answer on the right side of the equation. So, starting with the first two equations, let’s test this out:
11 × 11 becomes (1+1)(1+1), which becomes (2)(2), and 2 × 2 = 4.
Next, 22 × 22 becomes (2+2)(2+2), which becomes (4)(4), and 4 × 4 = 16. That’s also the answer we have already been given, so this method is consistent.
So, apply this same method for the third and final equation:
Answer 2: 33 × 33 = 18
This second method is called the “sum of the digits in the product.” Let’s break it down.This method involves simply multiplying the left side of the equation and then taking the product and adding together all of its digits. You will see that this works for both of the first two equations:
11 × 11 = 121, then taking the product and adding its digits, 1+2+1 = 4.
Likewise, 22 × 22 = 484, then 4+8+4 = 16.
Bonus Answer: Our Method 33 × 33 = 36
We managed to get the answer of 36 as well, but by a different means. By simply multiplying the left side of each equation, we took the ratio of the product and the answer on the right side of the equation as our pattern. We noticed that this ratio is the same for the first two equations, so we knew we had a pattern. Then we solved the third equation using simple algebra. Thus:121/4 = 484/16 = 1089/?
30.25 = 30.25 = 1089/?
30.25 = 1089/36
“Answer before watching the video 36. Edit: I knew it, I was right,” wrote one confident viewer.
“36, this is light work,” wrote another.
“I got [it] in 10 seconds,” someone else agreed, “and all his other puzzles stumped me.”
Then came the voices of dissent. “It’s impossible,” wrote one viewer. “If you have more than one answer you have no answer.”
“There can be more than one answer to such questions. There are no conditions attached to this question,” another person contributed. “Hence, no answer is right or wrong!”
Many people were left baffled and joked about the complexity of the puzzle. “Goodness, now my brain hurts,” wrote one person.
“The correct answer is putting a cross through all the equals signs,” joked another.
Some people, however, reveled in the fun and walked away feeling as though they had conquered the conundrum. “Finally got one of these right,” wrote one viewer, “feels good to be a genius lol.”
A third option for solving this puzzle, based upon the principles of Vedic multiplication, was also shared in the video (a word of warning: math-heads only; this option is not for the fainthearted!).
Which approach do you think is the best for solving this puzzle? The debate continues.
