# Cogwheels

The machine is broken! In order to get it working again, all cogwheels need to be placed in the correct places.

In this diagram a number of cogwheels have to be placed, such that they all spin when you spin one of them. Two cogwheels are connected if and only if the middles of their sides touch and they never overlap. The digits to the right and below the grid indicate how many squares are in use in that particular row or column. Furthermore it's given how many cogwheels of each size are in this puzzle.

## Example

As an example we will solve a small instance of these puzzles. Assume we're dealing with a puzzle with one wheel of size 3 and three of size 1.

We could ask ourselves where the wheel of size 3 could fit. Clearly not in the rightmost column and neither on the last row, so we immediately know the right position! The three remaining wheels should be somehow connected to this larger cogwheel, directly or indirectly, so there are two places of which at least one is taken (namely below the big wheel in the middle or in the middle to the right).

The numbers 4 instantly reveal now where the smaller wheels have to be, but suppose we ignore that fact for a moment and we take a look at the number 1 on row 4, then we notice that the only wheel on that row can not be in column 1, because you can not possibly connect it to the larger wheel from there. Column 2 is not a problem, but also the other two positions are invalid because the larger wheel is unreachable from there regarding the 1 square limit of that row and the 2 square limit in the rightmost column.

## Background

This genre was invented by Johan de Ruiter and puzzles of this kind have been published in Breinbrekers, a popular Dutch magazine for logic puzzles, frequently since December 2004.

Puzzles in this genre.
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