A particular cattle is fed $7 \text{kg}$, $8 \text{kg}$ and $9 \text{kg}$ of special food on Day $1$, $2$ and $3$ respectively by a farmer. From Day $4$ onwards, the amount of food fed to the cattle follows the following rule:  (i) if the total amount of food fed to the cattle in the past $3$ days is $24 \text{kg}$ or more, the cattle will be fed $2 \text{kg}$ less than the day before.  (ⅱ) if the total amount of food fed to the cattle in the past $3$ days is less than $24 \text{kg}$, the cattle will be fed $1 \text{kg}$ more than the day before.  Calculate the minimum number of days for the total amount of food fed to the cattle to exceed $2018 \text{kg}$. 
Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation
Amount of food fed to the cattle follows the pattern:  $789756$~ ~ $$789756$$~ ~ $789756$~ ~ $789756\cdots\cdots$  Total amount of food fed in the first $6$ days$=42 \text{kg}$.  $2018 =48\times6+1= 289$. 