Cogwheel Quandary
A puzzle in pencil. Someone sketched a machine and left the meshing blank: the posts, the crank and the needle are there — which gears go where is yours to draw. Teeth decide who touches whom; the needle tells you whether you built the machine the sketch asked for.
Every gear is a number.
A gear with twelve teeth has a radius of twelve; two gears on the same plane
mesh when their teeth add up to exactly the distance between their posts. One
more and they grind. One less and they miss. Nothing is declared — it all
follows from the sizes you choose.
The crank never stops.
Put a gear on a post and whatever it reaches turns. Build a chain from the
crank to the needle and the needle turns too — at whatever rate you built.
Beside it, a dashed ghost turns at the rate the sketch asks for. If they part
ways, you built a machine that works and is wrong.
Thirty machines, three rings each.
Small mechanisms around the edge of the sheet, one fewer a ring in, one big
one at the centre — and one tray shared by all of them, so two mechanisms can
want the same gear.
Free Draw.
Thirty more sheets with nothing on them but a crank, a needle and a target:
any gear on any post, either plane, two on one post for a stepped pair. The
fewest gears wins.
Drawn in graphite on paper, lettered by hand, scored by a music box over a
clock. Every sound and every tune is made inside the game — there is not one
sample and not one texture in it.