Only for geniuses? No, finding the answer doesn't mean you're a genius, but these puzzles from Facebook can still be fun

I just came across another one of these puzzles on Facebook the other day. You may already know that I love a good puzzle. Ones like you see here are usually quick and fun. In the puzzle above we have this problem:

111 = 13
112 = 24

113 = 35

114 = 46

115 = 57

117 = ??

In this case, the solution could be 79. But you knew that, right?

These kinds of problems can often have multiple solutions. Some of them are easy and some of them require a bit of work.

The above problem has two little tricks. Firstly, you have to notice the pattern for each operation (the equality symbol in this case does not imply that the left and right are equal, but that there is some operation that can be done to one side to make it equal to the other). To get my answer, the last digit on the left of the equality symbol can be taken as the first digit on the right. The second digit on the right is then the sum of all of the digits on the left. However, the second little trick in this problem is to then skip 116 = 68 and go straight to 117 = 79. Ya, not a big shocker there at all.  Like I said, quick and fun.  

Here are some more of these types of puzzles
(can you figure out answers for all three?):

So, what'd you get for your answers? My answers are, in order:

90, 410, and 143547 (though there are other answers!)

I posted those three problems with an order of increasing difficulty, but they're all still quite manageable since they all follow the same idea as the problem that started this post: namely, assume that the equality sign implies an operation is necessary to form one of the numbers from the other. If you're curious to now how I got my answers to those three problems, then you can cruise down to the bottom of this post. 

Before I get to that, however, I want to point out that answering these questions correctly does not make you a genius, nor should you believe the statistics that claim that only some number of people can get the answer correct.

Only for Geniuses?

Something that really bothers me about these types of puzzles on Facebook is that so many of them say something like "Only for Geniuses" or "Only geniuses will get the answer". What's with that? It may seem a bit silly to think that anyone would feel like they are somehow a certified genius just for answering a very simple problem just because some text on the problem said so, but I wonder how many people really do. How many people out there are swindled by such claims? 

I guess the important question is what exactly is a genius? A quick search online will reveal that there is no well-constrained definition of genius. Dictionaries may give some definition for genius, such as "an exceptional natural capacity of intellect, especially as shown in creative and original work in science, art, music, etc." from Dictionary.com. You might also see definitions claiming that genius implies having a high Intelligence Quotient (IQ). But scoring high marks on a standardized test is probably not the best way to judge. 

It's seems fairly well agreed upon that all people who are recognized as geniuses can score fairly high on tests of logic and reason, but they don't necessarily have to have the highest scores. Richard Feynman, one of the greatest physicists and thinkers of the past century, self-reported that his IQ was only ever measured as high as 125. 

The word genius should be used to imply respect for someone who has shown their mental prowess with mathematics, art, science, creativity, oratory, or teaching, but surely it's not something that can be determined from a simple puzzle on Facebook. That's absurd. Maybe the people who add the "only geniuses" text to those Facebook puzzles are just misled about what "genius" implies, but it's more likely that they're pandering to others in the hopes to increase the "likes" and "shares" of their images. I think the latter seems more likely. Indeed, it's become pretty common for people to use pandering techniques on social media to try to improve their internet presence.

So, what's the point? Why do I care so much? 

I think the "only for geniuses" crap bothers me because I love puzzles, but I don't like having my intellect attacked by pandering. Finding the answers to these puzzles on Facebook doesn't make you a genius, but the people who actually believe that are most likely not geniuses. Even a genius can be suckered into something stupid once in a while, but I think a measure of genius is having the ability to recognize when you're being cajoled.

There's a quote that goes "Everybody is a Genius. But If You Judge a Fish by Its Ability to Climb a Tree, It Will Live Its Whole Life Believing that It is Stupid".  This quote is often misattributed to Albert Einstein though it was likely written in this form first by someone named Matthew Kelly. Is everyone a genius in their own way? I'd like to think so, but the problem with being a genius is that it's only a quality in a person that can be recognized by others. If you want to be a genius, don't worry about what some pandering asshole wrote on a Facebook image, but rather find what you're good at and use that to make the world a better place.

We need a society of people who are literate in statistics

One other crappy thing about some of these Facebook puzzles is when they throw out some ridiculous faux statistic about how few people get these things correct. For instance, the claim that "Only 20% will give right answer on 1st attempt" on the first problem in this post is laughable. Where did they derive such information? Nowhere, of course. They made it up because it sounded impressive and because, once again, they're pandering to people who can be won over through emotional wheedling.

Todd Snider has a song called "Statisticians Blues" where he points out that "...64% of all the world's statistics are made up right there on the spot. 85.4% of people believe them whether they're even accurate statistics or not." Check out that tune here:

What do you think? Are 72% of all statistics really made up right there on the spot? Are you one of the 80.4% who will believe those made up statistics whether they're even accurate statistics or not?

You might have noticed that none of those values matched, and you might have also noticed many times in your life when someone tries to throw some numbers at an opinion to make it sound stronger without having the ability to say where those numbers came from. So what's up with that? 

Statistics is a field of study that focuses on how to qualify and quantify data in a rigorous manner. It's about learning from measurable data and making predictions from known evidence. Statistics is very much a scientific approach to considering data, yet it's constantly misused, especially in our era of data overload.

Misusing statistics is just another form of pandering on these Facebook puzzles, just like the "only for geniuses" claims. These fake stats are an attack on your intellect and your reason, but also on your emotions. Don't fall victim to the wheedling of the people who don't understand statistics! We should all take a little time in our lives to be sure we understand the "writing on the wall"; statistics literacy should be a common goal of all peoples' education in our modern world.

Okay, okay, enough ranting

Here's how I found my answers to those three problems earlier in the post:

How did I get the answers of 90, 410, and 143547?

Let's step through each one and see if you agree with me (again, there are usually many ways to solve these problems, and they often include breaking some of the "rules" of mathematics to do so):

Here's the easy one

This one is very simple. The problem is:

2 = 6 

3 = 12

4 = 20

5 = 30

6 = 42

9 = ??

Just as with the first problem in this post, the idea is to forget what you know of the equality symbol (it doesn't imply equality here, but rather what must be done to the numbers on one side to make them the numbers on the other side). You should hopefully see rather quickly that the operation is to take the number on the left and multiply it by the integer that is one greater than itself (so multiply 2 by 3 to get 6, 3 by 4 to get 12, and so on...). Once you see that you should find that the final answer (??) is 9 multiplied by 10, or 90. 

It's nice to get the right answer, but fun puzzles are definitely not only for geniuses.


Update (13 June 2015): 

Someone left a comment on this post today. They found an answer for this problem of 36, and I love their approach. Here's the comment they left:

f(z) = z * | |z-6| -7|
2 = 6
3 = 12
4 = 20
5 = 30
6 = 42

9 = 36

As you can see, this approach works perfectly well for this problem. Although this one isn't as easy to "see" by looking at the problem, it's still completely valid.

How about this one?

This one takes a little more thought, but it's not terrible. The problem is:

5 + 3 = 28  

9 + 1 = 810

8 + 6 = 214

5 + 4 = 19  

7 + 3 = ???

Remember my answer was 410? Beyond having to think beyond the normal use of an equality symbol, this problem requires you to break your usual thinking of how numbers are arranged. You need to perform some operation to the numbers on the left to make the numbers on the right, but you don't have to follow the normal rules of mathematics and you don't have to consider a string of numbers to be one unique number. What if I told you to think of these numbers like each one is separate? How does this look?

<5> <3> = <2> <8>

Any better? What if I just said "you have to do something with a 5 and a 3 that can give you a 2 and an 8"?

Did you think that the difference of 5 and 3 is 2 and the sum of 5 and 3 is 8? If so, then you're on the right track. 

Applying that thinking to the rest of the problem shows you:

The difference of 9 and 1 is 8 and the sum of 9 and 1 is 10:

9 + 1 = 810

The difference of 8 and 6 is 2 and the sum is 14:

8 + 6 = 214

Following that convention to the unknown gives you, "the difference of 7 and 3 is 4 and the sum of 7 and 3 is 10", hence my answer of 410:

7 + 3 = 410

Don't worry if you didn't get it. That whole "99% People Failed to Solve this Question" malarky is just a bunch of bunk!

Now for the tricky one:

This one may look pretty intimidating, and, admittedly, it took me a couple minutes to figure out.  Here's the problem:

5 + 3 + 2 = 151022

9 + 2 + 4 = 183652

8 + 6 + 3 = 482466

5 + 4 + 5 = 202541

7 + 2 + 5 = ??????

My answer for this problem is 143547. Notice how it has 6 digits? Did you notice how all the other answers have six digits? That's a pretty important feature of this problem.

This is one where you have to look at the numbers available on the left and start trying to figure out the potential associations to single numbers, strings of numbers, and the whole numbers on the right. Doing this, one thing I noticed right away was that the first line has 5, 3, 2 on the left and it has 15 (the product of 5 and 3) as well as 10 (the product of 5 and 2). If you take a look at the rest of the lines, this relationship holds; product of first and third numbers followed by the product of the fist and third numbers. Let's make some notation to explain this.  Let's set a line up as:

A + B + C = xxyyzz

Then, from what I've said so far:

A*B = xx

and

A*C = yy

That just leaves "zz". You may want to think about that one for a moment. Try combinations of A, B, and C using general arithmetic. I'll post the final answer below, but here's a fun cartoon first:

Get more giggles at Explosm.net

Still hanging around? This is a pretty long post, but, if you love puzzles and games as much as I do, then I hope you've found it worth your while. So here's how I found the final answer:

In the first line we get the product of 5 and 3 (15) and the product of 5 and 2 (10) and, if we're looking close, we have 22 yet to figure out, which is pretty close to 25 (the sum of 15 and 10). In fact, 22 is 3 less than 25, which led me to my answer:

For A + B + C = xxyyzz

where A*B = xx

and A*C = yy,

we can find that zz = A*(B+C) - B

or, in other words, zz = xx + yy - B

Now using the numbers from the problem:

7 + 2 + 5 = (7*2) / (7*5) / (7*(2+5) - 2) = 14 / 35 / 47

and, finally:

7 + 2 + 5 = 143547

Finding this answer will not make you a genius and no one has any idea about how many people have successfully solved this problem (or have even run any tests on an adequate sample to statistically say roughly how likely you are to be capable of solving it compared to the general public). Still, if you're like me, then you've probably at least had some fun working on the answers. 

Feel free to comment on these problems, my approach to solving them, or suggest some more fun puzzles!