Three participants - Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between $1$ and $9$. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants' scores on that day. The $2$-day average on a day, except on Day $1$, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day $1$ and Day $2$ are $25$ and $20$, then the $2$-day average on Day $2$ is calculated as $22.5$. Table $1$ gives the $2$-day averages for Days $2$ through $5$.
| Table $1: 2$-day averages for Days $2$ through $5$ |
| $\mathbf{Day2}$ |
$\mathbf{Day3}$ |
$\mathbf{Day4}$ |
$\mathbf{Day5}$ |
| $15$ |
$15.5$ |
$16$ |
$17$ |
Participants are ranked each day, with the person having the maximum score being awarded the minimum rank $(1)$ on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score $8, 7$ and $7$ respectively, then their ranks will be $1,2$ and $2$ respectively on that day. These ranks are given in Table $2$.
| Table $1-2$: Ranks of participants on each day |
| |
$\mathbf{Day1}$ |
$\mathbf{Day2}$ |
$\mathbf{Day3}$ |
$\mathbf{Day4}$ |
$\mathbf{Day5}$ |
| Akhil |
$1$ |
$2$ |
$2$ |
$3$ |
$3$ |
| Bimal |
$2$ |
$3$ |
$2$ |
$1$ |
$1$ |
| Chatur |
$3$ |
$1$ |
$1$ |
$2$ |
$2$ |
The following information is also known.
- Chatur always scores in multiples of $3$. His score on Day $2$ is the unique highest score in the competition. His minimum score is observed only on Day $1$, and it matches Akhil's score on Day $4$.
- The total score on Day $3$ is the same as the total score on Day $4$.
- Bimal's scores are the same on Day $1$ and Day $3$.
What is Akhil's score on Day $1$?
- $6$
- $7$
- $5$
- $8$