Chocolate

There were a few complete solutions sent in and many who showed us what the final result at the tables would be, i.e. $5$ at the $1$ table, $10$ at the $2$ table and $15$ at the $3$ table.

The full solution showing fractions at each stage were received from Adriel, Emily and Aswaath from the Garden International School in Maylasia. Also Daniel at Staplehurst School and Megan at Twyford School. Here is Emily's contribution. 

Nrich Solution
So after child $9$ has sat down, there are now:
$2$ people at table $1$
$3$ people at table $2$
$4$ people at table $3$
This is a list of which table child $10-30$ would go to:
The reason I listed down which table they would go to is to see whether there was a pattern
Child $10$ would go to table $3$ and receive $¾$ of the chocolate
Child $11$ would go to table $3$ and receive $½$ of the chocolate
Child $12$ would go to table $2$ and receive $½$ of the chocolate
Child $13$ would go to table $3$ and receive $3/7$ of the chocolate
Child $14$ would go to table $2$ and receive $2/5$ of the chocolate
Child $15$ would go to table $3$ and receive $3/8$ of the chocolate
Child $16$ would go to table $1$ and receive $1/3$ of the chocolate
Child $17$ would go to table $3$ and receive $1/3$ of the chocolate
Child $18$ would go to table $2$ and receive $1/3$ of the chocolate
Child $19$ would go to table $3$ and receive $3/10$ of the chocolate
Child $20$ would go to table $2$ and receive $2/7$ of the chocolate
Child $21$ would go to table $3$ and receive $3/11$ of the chocolate
Child $22$ would go to table $1$ and receive $¼$ of the chocolate
Child $23$ would go to table $2$ and receive $¼$ of the chocolate
Child $24$ would go to table $3$ and receive $¼$ of the chocolate
Child $25$ would go to table $3$ and receive $3/13$ of the chocolate
Child $26$ would go to table $2$ and receive $2/9$ of the chocolate
Child $27$ would go to table $3$ and receive $3/14$ of the chocolate
Child $28$ would go to table $1$ and receive $1/5$ of the chocolate
Child $29$ would go to table $2$ and receive $1/5$ of the chocolate
Child $30$ would go to table $3$ and receive $1/5$ of the chocolate
So now there are:
$5$ people in table $1$
$10$ people in table $2$
$15$ people in table $3$
I found out a pattern from child 10 to child $30$. When it was child $16$’s turn to decide which was the best place to sit, child $16$ could just choose to randomly sit on any table because he’ll still get $1/3$ of the chocolate in any of the tables. Same with child $22$ and $28$. Child $22$ would either ways get $¼$ and child $28 1/5$. The numbers also increase by $6. 16, 22, 28$.
I noticed that sometimes there were tables that shares the same amount of chocolate so you could choose randomly between $2$ or all of the tables which was what I did when I tried finding out how many chocolates each child receives as they go to find the best table for them
For example: Child $16$ gets to choose between any of the $3$ tables because he’ll still get $1/3$ of the chocolate in any of the tables

Well done all of you for your work on quite a difficult challenge.