Hey this is Presh Talwalkar. This problem
has been shared millions of times on Facebook and Twitter with the claim that
99% failed to solve it, and that only a genius could find the correct answer. In
this video I'm going to explain what many people believe to be the correct
answer. Can you figure it out? Give this problem a try. And when you're ready, keep watching the video for the solution. So most people believe the correct answer is 6. The pattern is to take the number on the left hand side of the equation and multiply it by 1 less than itself. For example the first line would read 9
times 8 which equals 72. The next line would be 8 times 7 which equals 56. We then have 7 times 6 which equals 42. 6 times 5 which equals 30. 5 times 4 which equals 20. And finally we would have 3 times 2 which equals 6. But not everyone believes 6 is the correct answer. Some people argue the correct answer is 12. They identify a pattern of decreasing subtraction in the number on the right hand side. So let's see how this pattern works. We start out with 9 equals 72. To get to the next line we subtract by 16 to get to 56. So that is why 8 equals 56. Now how do we get to the next line?
Rather than subtracting by 16 they would say you should decrease the amount
you're subtracting by to be 14. So then we have 56 minus 14 equals 42. This gives us the next line of 7 equals 42. We now subtract by 2 less so we have 42 minus
12 which equals 30. And that gets us to the next line. We
then subtract by two less again so we have 30 minus 10 which equals 20. So we
have 5 equals 20 and then we want to subtract by 2 less which will be 8. And
that will be 20 minus 8 which equals 12. And that's why they argue the answer is 3 equals 12. But hold on! There's a third group of people who say the answer is neither 6 nor 12 but actually that the answer is 9. Their method is looking at a pattern of decreasing multiplication. So this is very much like the answer being 6. You multiply a number by one less than itself. The difference in this method is now
they say look at the numbers you're multiplying by. This is a sequence of
numbers. We have 8, 7, 6, 5, and 4. So this group of people argues that
if you decrease this you would get the next line, which means you should
multiply the next line by 3. So they would say the answer is 3 times
3 which equals 9. So now let's recap the three different answers. Some people say the answer is 6; other people say the answer is 12; and even
other people say the answer is 9. Now it's a common question which of these answers is correct. Is there a more correct answer than any of the others? Well from the information we're given in the puzzle we can't definitively say. But what we can do is we can ask: is any of these answers is justifiable under the
patterns of the given methods? And by that standard, the answer of 6 is
justifiable by the two other methods. We can actually reconcile this to show that 6 is a very reasonable answer. How can we do that? Let's start out with the logic of the decreasing subtraction. So here's the information of the pattern.
Each time you're subtracting by 2 less than before. So now the question is: is there, or are there any other patterns, in this? Well
what you can do is focus on the first number in each line. We have a sequence
here. We have 9, 8, 7, 6, and 5. By this logic--that we should have a
sequence--we should then have a sequence that the next line be 1 less than 5.
So the next line should be 4. And by the logic of decreasing subtraction we would then have 4 equals 12. So then how do we figure out what the next line is? How do we get to what 3 equals? Well we look at the numbers we're
subtracting by. If we have this logic of decreasing subtraction we should subtract by 2 less than 8 so that means the next line would have 12 minus
6. And that would give us the answer on the right-hand side of the next line
which equals 6. So if we decrease 4 we then have the next line being 3 and then
we have the answer of 6 by this decreasing subtraction method. So once
again we figured out that 3 equals 6 and the answer is 6 by the very same
decreasing subtraction method. The only thing we had to do is we had to add the missing line of 4 equals 12. We can use the same kind of logic for the
decreasing multiplication method. Here's the information from the pattern which they argue about the decreasing multiplication method. So we're supposed to be looking for a logic to this--these numbers. But what we can do--is--we can
look at the first number in every single line. We have a sequence here of numbers
9, 8, 7, 6, and 5. So logic would suggest the next line should start out with 4. We then look at the numbers that we are multiplying by and that's another sequence 8, 7, 6, 5, & 4. So logic would suggest the next line should be multiplied by 3. So the next line should be 4 multiplied by 3 equals 12. If we continue this pattern the first number will be one less and the second
number will be one less so the next line would be 3 times 2. And once again
3 times 2 equals 6. So we again have the answer being equal to 6. This is even true under the decreasing multiplication method as long as we include the missing line of 4 times 3 equals 12. So to recap: it doesn't matter which method we're using. We're always going to get to the answer that 3 equals 6. And in fact we would have 4 equals 12 in each of these methods too. So this logic would suggest that the correct answer to this puzzle is that 3 equals 6. What do you think? Thanks for watching this video! Please subscribe to my channel, I make videos on math and game theory. You can catch on my blog MindYourDecisions which you can follow on Facebook Google+ and Patreon. You can catch me on social media @preshtalwalkar And if you like this video please check out my books! There are links in the video description.
