not next doors

join the numbers 1 to 4 (at the corners of a square) with 3 connectors so that joined numbers are not 'next door' numbers (i.e. 2 is not joined to 1 or 3)

is this the only way that you can do this?






join the numbers 1 to 5 with 6 connectors so that connected numbers are not 'next door' numbers

any other ways?

numbers 1 to 6 with 10 connectors?

prove that there are essentially two different solutions for an arrangement around a hexagon

why triangular numbers for the numbers of connectors?