MathDB

On Qingqing Grassland, there are 7 sheep numberd

1,2,3,4,5,6,7

and 2017 wolves numberd

1,2,\cdots,2017

. We have such strange rules: (1) Define

P(n)

: the number of prime numbers that are smaller than

n

. Only when

P(i)\equiv j\pmod7

, wolf

i

may eat sheep

j

(he can also choose not to eat the sheep). (2) If wolf

i

eat sheep

j

, he will immediately turn into sheep

j

. (3) If a wolf can make sure not to be eaten, he really wants to experience life as a sheep. Assume that all wolves are very smart, then how many wolves will remain in the end?

Problem Statement