Does this look familiar?

SOLVE IF YOU ARE A GENIUS! 99% OF PEOPLE WILL GET IT WRONG!

8 = 56

7 = 42

6 = 30

5 = 20

3 = ?

No doubt every time you've seen this on

Facebook, it's followed by thousands upon thousands of responses,

each indignant that other people are getting the wrong answer.

Generally there are two or three different numbers that keep coming

up, with nobody able to see how anyone else could have gotten a

different answer from their own.

I hate these things.

These things are designed to be vague. There is no answer, or rather,

SOLVE IF YOU ARE A GENIUS! 99% OF PEOPLE WILL GET IT WRONG!

8 = 56

7 = 42

6 = 30

5 = 20

3 = ?

No doubt every time you've seen this on

Facebook, it's followed by thousands upon thousands of responses,

each indignant that other people are getting the wrong answer.

Generally there are two or three different numbers that keep coming

up, with nobody able to see how anyone else could have gotten a

different answer from their own.

I hate these things.

These things are designed to be vague. There is no answer, or rather,

there are an infinite number of answers. The crux of the issue here is

that

So these things are basically a weird

way of presenting a function. You remember functions from my

previous blog post, right? Well, essentially what this thing is

saying is “you take 8, do some mystery function to it, and you get

56. Et cetera, et cetera, what do you get when you use 3?” The

problem is that there are multiple rules that could apply here, so

you have no idea what function they actually gave you and therefore

cannot answer the question.

Here's our example from above, showing

two different rules that could be used to create the list:

FIRST OPTION

y = x * (x-1)

56 = 8 * (8-1) = 8 * 7

42 = 7 * (7-1) = 7 * 6

30 = 6 * (6-1) = 6 * 5

20 = 5 * (5-1) = 5 * 4

**they don't define the rule.**So these things are basically a weird

way of presenting a function. You remember functions from my

previous blog post, right? Well, essentially what this thing is

saying is “you take 8, do some mystery function to it, and you get

56. Et cetera, et cetera, what do you get when you use 3?” The

problem is that there are multiple rules that could apply here, so

you have no idea what function they actually gave you and therefore

cannot answer the question.

Here's our example from above, showing

two different rules that could be used to create the list:

FIRST OPTION

y = x * (x-1)

56 = 8 * (8-1) = 8 * 7

42 = 7 * (7-1) = 7 * 6

30 = 6 * (6-1) = 6 * 5

20 = 5 * (5-1) = 5 * 4

So

y = 3 * (3-1) = 3 * 2 = 6

This is the answer that a lot of people

get because it's a bit more obvious. It's also the first answer that

jumps out at me. But there's a second option:

SECOND OPTION

n

n

y = x * n

This second option is more of a

programming-type sequence, but no less legitimate. In this case, n

means “the value of n for any given term t.” The rule given for

finding n

value counts down by 1. n

puzzle, as is common with rules of this type. This means the rule is

no longer relative, but absolute. No matter what first x value you

choose, the first n is 7. The second n is 6, the third is 5, and so

on. By this logic the beginning is still correct:

56 = 8 * 7 First Term: t = 1, n

42 = 7 * 6 Second Term: t = 2, n

30 = 6 * 5 Third Term: t = 3, n

20 = 5 * 4 Fourth Term: t = 4, n

y = 3 * (3-1) = 3 * 2 = 6

This is the answer that a lot of people

get because it's a bit more obvious. It's also the first answer that

jumps out at me. But there's a second option:

SECOND OPTION

n

_{1}= 7n

_{t}= n_{1}- (t-1)y = x * n

_{t}This second option is more of a

programming-type sequence, but no less legitimate. In this case, n

_{t}means “the value of n for any given term t.” The rule given for

finding n

_{t}works out to mean that after each term, the nvalue counts down by 1. n

_{1}would be set to 7 by thepuzzle, as is common with rules of this type. This means the rule is

no longer relative, but absolute. No matter what first x value you

choose, the first n is 7. The second n is 6, the third is 5, and so

on. By this logic the beginning is still correct:

56 = 8 * 7 First Term: t = 1, n

_{t}= n_{1}– (1-1) = n_{1}- 042 = 7 * 6 Second Term: t = 2, n

_{t}= n_{1}– (2-1) = n_{1}- 130 = 6 * 5 Third Term: t = 3, n

_{t}= n_{1}– (3-1) = n_{1}- 220 = 5 * 4 Fourth Term: t = 4, n

_{t}= n_{1}– (4-1) = n_{1}- 3BUT THEN

y = 3 * 3 = 9 Fifth Term: t = 5, n

With this version you get 9 instead of

6. Why is that, when the other terms are all the same?

_{t}= n_{1}– (5-1) = n_{1}– 4, so 7 – 4, or 3With this version you get 9 instead of

6. Why is that, when the other terms are all the same?

Notice they left out x = 4 in the

puzzle – it jumps straight from 5 to 3. If we were using the first

rule it wouldn't matter, since the rule is only relative to the

current x value and will work no matter where in the sequence a given

number finds itself. You could shuffle the lines around to your

heart's delight and the answers would still be the same. But this

version is what's known as a “recursive” sequence, where the rule

depends on where the term is in the sequence, and moving the terms

around will change the results drastically. What looks like a

logical sixth step is actually the fifth term in the sequence.

If we put 4 in for x where it looks

like it should be, it changes how you find the result of each term

thereafter. Then we'd have:

20 = 5 * 4

12 = 4 * 3

6 = 3 * 2

So we'd get the same answer as the

first option. But that's assuming they've left out a term, which you

can't be sure of since they didn't tell you that explicitly. To

assume that is simply to be a sloppy mathematician, and sloppy math

leads to incorrect math. Here is what they would have had to show

you for that to be the case:

n

n

n

n

n

By showing you that it jumps straight

from the fourth term to the sixth, they're letting you know the

counter should have ticked down one additional time, and at that

point you will be able to solve the problem. But not without that

additional piece of information.

So here I've shown two legitimate ways

to solve this badly-written problem, getting two completely different

answers. Since the issue is that the problem is not specific enough,

the only prudent answer to these questions is always “There is not

enough information given.”

I hate these things because they are

intentionally vague. The people who make these problems (or at the

very least the people who post them on Facebook) likely don't realize

just how complicated the problem is. Most people will only see one

solution, so it will appear easy and they won't be able to understand

how someone else got 9 when it's “obviously” 6. This leads to

arguing futilely over something which, to any mathematician, is just

a problem that's so badly-written it's useless. No mathematician

worth her salt would ever write a sequence that way anyway, so why

argue about it?

puzzle – it jumps straight from 5 to 3. If we were using the first

rule it wouldn't matter, since the rule is only relative to the

current x value and will work no matter where in the sequence a given

number finds itself. You could shuffle the lines around to your

heart's delight and the answers would still be the same. But this

version is what's known as a “recursive” sequence, where the rule

depends on where the term is in the sequence, and moving the terms

around will change the results drastically. What looks like a

logical sixth step is actually the fifth term in the sequence.

If we put 4 in for x where it looks

like it should be, it changes how you find the result of each term

thereafter. Then we'd have:

20 = 5 * 4

12 = 4 * 3

6 = 3 * 2

So we'd get the same answer as the

first option. But that's assuming they've left out a term, which you

can't be sure of since they didn't tell you that explicitly. To

assume that is simply to be a sloppy mathematician, and sloppy math

leads to incorrect math. Here is what they would have had to show

you for that to be the case:

n

_{1}: 8 = 56n

_{2}: 7 = 42n

_{3}: 6 = 30n

_{4}: 5 = 20n

_{6}: 3 = ?By showing you that it jumps straight

from the fourth term to the sixth, they're letting you know the

counter should have ticked down one additional time, and at that

point you will be able to solve the problem. But not without that

additional piece of information.

So here I've shown two legitimate ways

to solve this badly-written problem, getting two completely different

answers. Since the issue is that the problem is not specific enough,

the only prudent answer to these questions is always “There is not

enough information given.”

I hate these things because they are

intentionally vague. The people who make these problems (or at the

very least the people who post them on Facebook) likely don't realize

just how complicated the problem is. Most people will only see one

solution, so it will appear easy and they won't be able to understand

how someone else got 9 when it's “obviously” 6. This leads to

arguing futilely over something which, to any mathematician, is just

a problem that's so badly-written it's useless. No mathematician

worth her salt would ever write a sequence that way anyway, so why

argue about it?

## Comments

If you got that one right ("go"), then you should be able to see why the only possible correct answer is 3.

Another clue would be that, as noted above, if you follow the herd in thinking that you are supposed to be looking for a pattern, then you can reasonably come up with almost an infinite numbers of equally reasonable answers.

There was no instruction to find or follow a pattern. Just a series of statements made to create misdirection, to throw you off from answering a simple question - like the example I gave with hop, pop & mop ....