Question 29
There are two fair dice and their sides are positive integers $a_1,\ldots,a_6$ and $b_1,\ldots,b_6$, respectively. After throwing them, the probability of getting a sum of $2,3,4,\ldots,12$, respectively, is the same as that of throwing two normal fair dice. Suppose that $a_1+\cdots+a_6\lt b_1+\cdots+b_6$. What is $a_1+\cdots+a_6$?