其它
Rabbit Borya likes cabbages and carrots very much. In a day he eats either 9 carrots, or 2 cabbages, or 1 cabbage and 4 carrots. During one week Borya has eaten 30 carrots. How mnay cabbages has he eaten during this week? 
Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Borya ate 30 carrots in a week, which is a number divisible by 3.  On the days that he ate 9 carrots, the total number of carrots is also divisible by 3.  Hence, the total number of carrots he ate on days that he ate 4 carrots must also be divisible by 3, meaning the number of days he ate 4 carrots is divisible by 3.  If there were no days he ate 4 carrots, he ate 9 carrots in 30/9 days, which is impossible. If there were 6 days he ate 4 carrots, he was left with only 30-6 x 4 = 6 carrots to eat on other days, which is also impossible.  therefore, he ate 4 carrots on 3 days, meaning there are \_\_\_ 2 days he ate 9 carrots. There were 3 days Borya ate 1 cabbage, and 7 \_ days he ate 2 cabbages.  He ate a total of 3 + 2~ x 2 = 7 cabbages in a week. 