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2 problems match “integer partitions”. Clear

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1. Three piles of coins with increasing sizes ●●●○○ 50 ptsFind the number of ways $66$ identical coins can be separated into three nonempty piles so that there are fewer coins in the first pile than in the second pile and fewer coins in the second pile than in the third pile.
2. Maximum smallest ball in bowl Jia ●●●●○ 100 ptsPlace the 27 balls numbered $1$ to $27$ into three bowls, Jia, Yi and Bing, so that the average ball number in bowl Jia is $15$, in bowl Yi is $3$, and in bowl Bing is $18$, and each bowl contains at least $4$ balls. Find the maximum possible value of the smallest ball number in bowl Jia.