# How many digits does the integer have?

We choose two numbers between $0$ and $9$, and the sum of the numbers should not be $9$. In addition, we cannot choose a number which we have already taken. How many digits does the sum have at most?

• Can I choose 8 and 9? Then the sum is at most of two digit? – Yujie Zha Mar 16 '17 at 3:46
• I have answered the asked question, but I wonder if it's what you intended. My answer has nothing to do with probability and doesn't use any of the assumptions of the problem other than "between $0$ and $9$" – Stella Biderman Mar 16 '17 at 3:48
• Well, the sum can not exceed $9+9=18$. – Rayees Ahmad Mar 16 '17 at 3:48
• I choose $e$ and $\pi$, with an infinite number of digits. – Joffan Mar 16 '17 at 3:48
• @Joffan,sir, the question is," How namy digits does the interger have?" – Rayees Ahmad Mar 16 '17 at 3:55

The sum of two one digit number is clearly less than $100$ and so cannot have $3$ digits. $6+5=11$ demonstrates that there can be $2$ digits, and so the answer is $2$.