May be this example will help: consider three rods connected to each other by pin joints. Once fixed, the three rods cannot move with respect to each other without deforming the other rods. On the other hand, if you have four rods of equal lengths connected to each other by pin joints, they can move with respect to each other without deforming themselves or the other rods. So the three rod system is statically determinate, while the four rod system is statically indeterminate.
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