I'm trying to understand the solution to a puzzle named "Expelled," the link to which is here. Most of the solution to the puzzle makes sense to me, except the most important part -- how to determine what the next line looks like based on the previous line! Speaking specifically, can someone please decipher for me the line "Starting at the expelled number in row n-1, row n is generated by writing the numbers positioned (-1,1,-2,2,-3,3,-4,4,…) away from the expelled number, as long as they exist, where negative numbers mean “to the left” and positive numbers mean “to the right.”"? Thank you!
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$\begingroup$ For anyone wondering: The puzzle "Expelled" itself consists of only the 9*18 and 2*11 tables shown in John's answer, and the title, "Expelled." $\endgroup$– retzlerJun 4, 2020 at 16:58
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As you can see above, the number $1$ is expelled in the first row. The number sequence $ (-1,1,-2,2,-3,3,-4,4,…) $ describes the relative position from the expelled number (assuming the number at the position exists). Now, number at position $-1$ for $1$ doesn't exist. So moving on to next, we get position $1$ which is 2. Obviously numbers at position $\lt 0$ doesn't exist for this. To make it more clear, we shall take the $5\text{th}$ row, here the number expelled is $4$ i.e. $5\text{th}$ number in the $5\text{th}$ row as stated. Now, \begin{array}{ | l | l | } \hline \text{Position} & \text{Number} \\ \hline -1 & 9 \\ \hline 1 & 10 \\ \hline -2 & 6 \\ \hline 2 & 11 \\ \hline -3 & 8 \\ \hline 3 & 12 \\ \hline -4 & 2 \\ \hline 4 & 13 \\ \hline \end{array}
in which the number column is clearly the next row.
