System Of Gears

Lets say that the first gear spins clockwise, then second would spin counter clockwise and so on and on.

We can generalize this by saying that for odd number of gear it would spin clockwise and for even - counter clockwise

For such system that is described to be spinning all together we need to have the first and the last gears spinning in opposite directions. However, we do not have that as 1 and 7 both are odd!

$Let\quad C\quad =\quad Clockwise\quad and\quad A\quad =\quad Anti-clockwise\\ Let\quad wheel\quad 1\quad is\quad rotating\quad Clockwise\\ 1=C\\ 2=A\\ 3=C\\ 4=A\\ 5=C\\ 6=A\\ 7=C\\ 1=A\\ at\quad last\quad we\quad can\quad see\quad that\quad 7\quad is\quad rotating\quad Clockwise\quad \\ which\quad make\quad the\quad 1st\quad to\quad rotate\quad Anti-Clockwise\quad \\ This\quad is\quad \boxed { Not\quad Possible } .$

First and the seventh gear will be spinning in the same direction