# Brain Teaser - How does 12=11?

The following statement is true:

12=11

There are no mathematical operators (+, −, *, /), exponents, parentheses, etc. missing. How can 12 and 11 be equal?

Hint 1: The given is not false.

Hint 2: How did the first humans count?

Tide
Homework Helper
Would your UserID be a hint? :)

$${\log_{12}}^{11}=x$$

Last edited:
is it one of two equals two of one?

Tide
Homework Helper
HINT: Think 9. :)

I hope the solution is more clever than these:

- the left number is in base 9 notation, or

- the right number is in base 11, or

- the left number is in base-3 while the right one is in base-4, or

- keep changing numeric bases without telling anyone...

:tongue2:

From what everyone else has said, I feel my answer was a bit unsual..would it be more like $${\log_a}^b+{\log_b}^c={\log_a}^c$$?

The second hint makes me think of counting with my fingers. when you count to two, you can either say "one two" (12) or "one and one" (11). Is that it?

arildno
Homework Helper
Gold Member
Dearly Missed
You may count spaces between your fingers, rather than the fingers themselves.
Doesn't make the number 12 equal to the number 11, though.

if the solution is simply changing bases then the problem is wrong because in math...you cannot write two bases without indicating one.

I would say that the first humans used thier fingers to count from 1 to 10, and anything above that would be considered "a lot of damn numbers". In this sense, they would consider 12=11=many :-)

The real "answer" is probably having changed based without indicating it though (which is cheating since you said nothing is missing).

...and bbarry9999 chuckled as he walked away, never to return after posting an impossible riddle...

JasonRox
Homework Helper
Gold Member
Orefa said:
...and bbarry9999 chuckled as he walked away, never to return after posting an impossible riddle...
I ignore One-Posters.

They are a waste of time.

Sometimes it can be an interesting discussion though, like that 1=0.999... thread. :grumpy:

12 is a name property.
11 is a name property.
the above two instances are properties of a common object.