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Hey everyone! Every once in a while, we like to do a little puzzle to keep you all on your toes. As you know, real estate investing is a numbers game, so we think “number games” are great diversions from the daily grind and keep your brain just a little fresher.

Here is a puzzle we found while scouring the internet for interesting, tricky puzzles that appear to have a simple solution at first but are inherently tricky. As with the 90% fail problem, this problem has a couple of different answers, depending on how you think of the problem. Get the math jumbled up, and you may have a different answer entirely.

80% fail to answer this simple math problem. Are you a “genius” or are you going to end up among the 80%? Take a look at this problem below.

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Let us know what you think. The survey results are listed below. If you really want to voice your opinion, as so many people did on 90% fail, we’d love to hear from you in the comments section as well!

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The answer is 11. Math is math. Regardless of the other answers, if someone asked you “What us eleven equal to,” then answer has to be elven, or some equation that is equal to 11. There is no function defined, and even if it was, it would have to be f(11). As it is stated, 11=11.

I would actually argue that 121 is correct. Although, I understand the reflexive property seems to hold here, the problem is this, 1 != 11. Not using standard definitions. Now, you could argue that the numbers are being redefined. But this is not, to my knowledge, ever done in math. However, what is far more often done is that operands are redefined. So, from that, the = does not mean equals as in its standard equality, but is a transformative operator. Transforming x -> 11x. Thus, 121 is valid. The reflexive property only holds valid with equality, which this, clearly is not.

At the end of the day, if the numbers are being redefined, it is that point at which math becomes truly broken. As stated earlier in the 90% problem: “Math is simply nothing but logic and you can’t ASSUME things that aren’t stated.” Here, you can’t assume the = is the standard equality operator. You could argue that I am making an assumption that the numbers aren’t variables, which is true, but that seems a more solid assumption in my mind as I have never seen numbers used to replace variables.

Fun, nonetheless.

Then what is 12 or 10

121

the answer is 1

I think the only true answer 11= ? is unsolvable. The problem as presented does not provide enough information to derive an answer without making an assumption.

To get 1111, you have to assume this is representing character substitution like as done in a simple cipher (a=b b=c, ab=bc)

To get 121, you have to assume they are really talking about applying a function to get the result (i.e.. f (1) = 11)

To get 11, you have to assume the other statements are false.

To get 1, you have to assume the numbers are actually variables (e.g. a=b so b=a)

Each of these require only one assumption to reach the result so can’t argue Occums Razor(the one with fewest assumptions must be selected).

The only possible answer left then is unsolvable based on the data given.

Very interesting point. Thanks for your comment and for checking out our blog!

The issue here is context.

Consider the first line: 1 = 11.

What does the first symbol 1 represent? If it represents the VALUE 1 (as in there is 1 “O” in “LOL”) then this statement is inconsistent, as the VALUE 1 cannot be equal to the VALUE 11 (as in Mississippi has 11 letters).

Therefore, 1 must, in this case at least, be some kind of symbol. Since the symbol X is not the same as XX, it is not inconsistent to say that X = XX or that 1 = 11, but we must be using 1 and 11 SYMBOLICALLY to represent some unknown values.

In this case, the rest of the equations must be sets of symbols as well, and while it is very uncommon to use numerals such as 1, 2, 3 … as representations of unknown values, it is not unprecedented. In early FORTRAN programs it was possible to use the command 2 = 4 to assign the VALUE 4 to the SYMBOL 2. But you can imagine the kind of trouble this caused, which is why latter version of FORTRAN flagged such instructions as errors.

So we have here a situation where 1 is like X and 11 is like XX. 1 and 11 are just names of unknowns and the symbols 1 and 11 are used to represent two unknown values just like X or XX might have done.

But this means that 2 = 22 and 3 = 33 etc. do not have any bearing on what 11 =. We could restate the entire question like this:

X = XX

Y = YY

Z = ZZ

A = AA

B = BB

C = CC

XX = ?

Here I am assuming the ? means “what does XX equal,” which considering the question is a significant assumption, given that we can’t even assume that the Symbol 1 equals the Value 1.

Nevertheless, we do have what we need to solve this problem. XX = X, as is indicated in the first line. But notice, we don’t need to know anything about any of the other symbols. Y, YY, Z, ZZ, A, AA, B, BB, C, and CC tell us nothing about what XX is equal to. Therefore, we can write the entire problem as:

X = XX

XX = ?

Now, let’s put back the 1’s for the X’s remembering that 1 is NOT a Value, but merely a Symbol.

1 = 11

11 = ?

Since there are only symbols here , and no values, we cannot determine the actual value of 11, but we can tell that it is equal to whatever the value of 1 is, as is indicated in the first line. Therefore:

11 = 1

This does not mean the VALUE 11 is the same as the VALUE 1, but rather that the Unknown variable that has the Symbolic name “11” has the same value as the Unknown variable that has the Symbolic name “1”.

Given that “1 = 11” is wrong if we presume they are values, this answer (“11 = 1”) is much better than “11 = 121”, which is also obviously wrong.

Cheers!

Why is 11=121 wrong? What if I assume that every time the number in column 1 increases by 1, the number in column 2 increases by 11? Are we to assume that this is not a pattern recognition problem?

Hahaha I say its 1 again because according to maths if u see out here they haven’t mention anything about the case but what we know is . 1=11

2=22

3=33

4=44

5=55

6=66

11=?

So this numbers mean they are equal to each other nothing more then that no multiply addition substraction, anything so if 1=11 then in terms of simple maths it should be 11=1

it could be either 1111 or 121 as each of the answers given are either the first number stated twice (5 = 55, 6 = 66, 8 = 88, 10 = 1010, 11 = 121) or the first number multiplied by 11 (5 * 11 = 55, 6* 11 = 66, 10 * 11 = 110, 11 * 11 = 121). Either answer is equally correct with the given information as there is no indication if the right said of the equation is due to multiplication of duplication. if one were to infer that one should divide both sides by the smaller number, then the answer would always be 11, suggesting multiplying by 11 is the only true answer.

oops, typo in my first parenthesis; 11 = 1111

I believe the answer is 7, perhaps?

1

I think its 121 because I realized it WAS multiples of 11. There is no numbers in the world besides 11 that multiplies like that! So I figured it MUST BE ELEVEN!

11 = 1 🙂 because 1=11 therefore 11=1 😀 😀

Yup. I also think the answer is 1111. ‘Cause, y’know, that digits is doubling!

1 = 11

2 = 22

11 = 1111

I think it is 1111

121

The first equation says 1=11.

The last equation says 11=?

We know 1=11 so 11=1.

It doesn’t matter which order you put it.

If a=b then b has to equal a.

It is just that simple.

The answers:

1=11×11÷11

2=22×22÷22

3=33×33÷33

4=44×44÷44

5=55×55÷55

6=66×66÷66

11=121×121÷121

Simple!

Simple

The answers:

1=1×11÷11

2=2×22÷22

3=3×33÷33

4=4×44÷44

5=5×55÷55

6=6×66÷66

11=11×11÷11

Simple!

The answers:

1=1×1÷1

2=2×2÷2

3=3×3÷3

4=4×4÷4

5=5×5÷5

6=6×6÷6

11=11×11÷11

Simple!

1=11

2=22

3=33

4=44

5=55

6=66

7=77

8=88

9=99

10=1010

11=1111

its 111 if 1=11 then 11=111 its simple just 1=11 right? Then add 1 to that 11

you see then you have it! Its simple and last that all whe waited for is

11=111

Numbers cannot be assigned as variables in computer coding without a symbol to declare them as variables. If 11 is a variable, then the value is 0 since it was declared, and given no value… that makes the answer 0, in both sum and equal. If you were thinking algorithmically, and assumed the premise that 11 was a declared variable, then the answer would be 121. If you were thinking that “=” meant “equal” instead of “sum” then you would get the answer of “1”. Since 1-6 treats numbers as both variables and values at the same time without such figurative symbolic declaration, one could assume that 11 should behave in the same manner, however there is nothing to say that this behavior is required for each line, so after thinking about it… the answer is 11, being that 11 is a value by default as it represents the tangible number 11 (yes, numbers are tangible), and is not declared as a variable in the problem.

11 = 11

If “1” is a global or constant variable, and “11” is it’s value, and “11” is a global or constant variable, and it has no value, then 11 = nothing.