Three Wrongs Make A Right?

No, it can't happen.

Let's first rewrite this equation:

$\frac{O_1}{O_2} \cdot O_3 = E$

$O_1 \cdot O_3 = E \cdot O_2$

$O_1, O_2$ and $O_3$ are all odd and $E$ is even. This means, we can write them in the following form, where $p, m, n, k \in \mathbb{Z}$ :

$(2p + 1) \cdot (2m + 1) = 2n \cdot (2k + 1)$ $4pm + 2p + 2m + 1 = 4nk + 2n$ $2 \cdot ( 2pm + p + m ) + 1 = 2 \cdot (2nk + n)$

This means: ODD x ODD = ODD and ODD x EVEN = EVEN .

This means again that our equation can never be true

any no. can be written as the product of its prime factors. an even number is a number having 2 as one of its factors. so all the three no.s in the question don't have 2 as its factors. hence their product or its quotient cannot be even

I Just used a extremely simple and useful mathematic principle $\frac { Odd }{ Odd } \times \frac { Odd }{ 1 } =Even\\ \\ 1\times Odd=Even\\ \\ Odd\neq Even$

You're doing arithmetic in $\mathbb{F}_2^\times$ on the left. Which is closed. The right is not an element of that group, so it is not possible.

Let $A, B, C$ be the odd numbers and $E$ be the even one. $\frac{A}{B} \cdot C = E \Rightarrow \frac{A}{B} = \frac{E}{C} = λ \Rightarrow \begin{cases} E = λ \cdot C \stackrel{\text{C is odd}}{\stackrel{\text{E is even}}{\Rightarrow}} λ = 2\cdot k (*)\\ A = λ \cdot B \stackrel{(*)}{\Rightarrow} A = 2\cdot \Bigg(k\cdot B\Bigg) \rightarrow \text(Contradiction!)\\ \end{cases}$

If 2 is a factor of the product, then 2 has to be a factor of either the multiplier or the multiplicand. Which is not the case here. One might ask, can (ODD/ODD) yield an even quotient? It cannot. Again, if the quotient is a multiple of two, then the dividend has to be a multiple of 2 too.

If (O1/O2) O3 = E, then, O1/O2 has to be a even number, because (Odd number) (Odd number) = (Odd number).

But if O1/O2 = E, then, O1 = O2 E. Thus O1 is an even number, because (Odd number) (Even number) = (Even number). This is an absurde!

Thus, (O1/O2)*O3 = E can never happen.

From the question " [Odd/Odd] x Odd = Even ". We get Odd x Odd = Odd x Even = Even. (multiply Odd) NONE of Odd number production can give even number. The answer is NO

3x3=9 x X = X= no

it's not right at all.

NO! Take the odd number as 1 . $\frac{1}{1}$ times 1 is 1 * !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! * THE ANSWER IS AN ODD NUMBER!!!!!!!!!!!

No, it can't happen. Cause, When we divide an odd by an odd that will also an odd number. so (Odd/Odd)=always Odd.And multiply of Two odd numbers is also an odd number.(Odd x Odd)=Odd So it can't happen.

Counter example: (21/7)*3 = 9 that is odd.

Genral form of odd is (2n+1) or (2n-1)

so if we take 2n-1 we get (2n-1)/(2n-1)*(2n-1) => (2n-1).. i.e.., Another odd number only.

Every odd number Is a multiple of 2 odd number If we divide with an odd number the number left is odd and then multiplying it by odd would result odd

Because when we divide any odd number by another odd number it will give odd number and multiply will be also an odd number.for e.g. (17/5)*7=an odd no.