Sum is even?

Question

Comments

i didn't understand what does this
"the minimum number..." means?

---

It means that first u divide given set into odd and even integers :

pick one-one integer from both of them, when u chose the third integer (from any of the set,)

the sum of two integers will be even (bcz u will be having EE or OO definitely)

Answer 1

Even numbers = $\{  2,4,6,8\}$

Odd numbers = $\{  1,3,5,7,9 \}$

Sum property =

Choosing $2$ numbers possibility = $\{EE,\color{Red}{EO},\color{Red}{OE},OO\}$

Example  $3+2=5$ Fail

Choosing $3$ number possibility = Use pigenhole no matter how you choose $3^{rd}$ number either will be $odd$ or $even$.
$\therefore$ Sum will be even.
Example $ {\{3,2\}}$ Choice $Odd$ or $Even $ lets say $5$ or $4$
Then , $5+3=8$ or $4+2=6$

Comments

Thanku so much. .now it is clear .  saxena0612 

---

yes,
it is min 3
because in case of 2 we can choose eg.(2,3) which is odd
but 3rd element if u choose say 4
So, here even pair is 2,4

---

Thanku so much  srestha