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$s$ | formula for $n$ | possible? |
$3$ | $3(n-4)=2n\\ 3n-12=2n$ |
$n=12$ (seen) |
$4$ | $4n-16=2n\\ 2n=16$ |
$n=8$ (seen) |
$5$ | $5n-20=2n\\ 3n=20$ |
no |
$6$ | $6n-24=2n\\ 4n=24$ |
$n=6$ (seen) |
$7$ | $7n-28=2n\\ 5n=28$ |
no |
$8$ | $8n-32=2n\\ 6n=32$ |
no |
$9$ | $9n-36=2n\\ 7n=36$ |
no |
$10$ | $10n-40=2n\\ 8n=40$ |
$n=5$ (seen) |
$n$ | $s=\frac{2n}{n-4}$ | comment |
$4$ | division by zero | This fits with Iqra's observation that you can use as many squares as you like |
$3$ | negative | In fact triangles do make a ring, but there is no shape in the middle |