Math Problem (Level 2) : Choose number from 1 to 10 by turns (LL14)

Two persons choose a number from 1 to 10 by turns and sum up all numbers both choose.

They may also choose the same number many times.

When the sum total of the number of two persons becomes 100 or more, the person who chose the number at last is to be loser.

When the first person chose 8, which number should be chosen next in order for another person to certainly win?


Answer
3

Solution
Another person should choose the number which comes to 11 of sum total every choice. 

It will be set to 11 × 9 = 99 at the 9th time and the last person will win.

Therefore, a number to choose is 3.