# _+_+_=30. What numbers can be used to fill the blanks? {1,3,5,7,9,11,13,15}

Aug 2, 2017

Not possible.

#### Explanation:

All the available numbers are odd.
The sum of 3 odd numbers must be odd as well.
30 is an even number.

Aug 2, 2017

No solution

#### Explanation:

We are only given odd numbers as addends, so we want to add three odd numbers to get an even number, $30$.

The sum of two odd numbers is an even number. This even number plus an odd number must result in an odd number because:

An even number plus an odd number is odd.

Therefore, an even number plus an odd number cannot be 30.

Aug 3, 2017

Turn the $9$ upside down to get the solution:

$6 + 11 + 13 = 30$

#### Explanation:

As the other contributors have mentioned, the sum of three odd numbers is always odd. We have to cheat in some way.

The only merit in questions of this sort is encouraging a little lateral thinking.

Aug 5, 2017

$\textcolor{g r e e n}{\left\{3 + 1\right\} + 11 + 15 = 30}$
color(green)({5+1}+9+15=30
color(green)({7+1}+9+13=30
Or $\textcolor{b l u e}{\text{not possible}}$

#### Explanation:

There's no solution if we got no brackets to insert. we can solve such questions only by using brackets as other contributors mentioned ,"sum of $3$ odd no.s can't be even". so this is the only possible way out or as mentioned in other answer . invert $9$ to get $6$ .

Without cheating, it's not possible because sum of three odd numbers can't be even.

Let $k$ be any real number.
So,
$2 k + 1$ will be an odd number & $2 k$ will be an even number.
Let $n , \text{ } m$ be some other random real numbers.

If we add $2 k + 1$,$2 m + 1$,$2 n + 1$ (all being odd numbers)
We get, $2 k + 2 m + 2 n + 3$

We know that $2 k , \text{ "2m," } 2 n$ are even numbers. So, $2 k + 2 m + 2 n$ is even and when you add an odd number to an even number we get an odd number.
So, it isn't possible...