Statements : Some boxes are hammers. Some hammers are beads. All beads are rings.

Conclusions :
I. Some rings are hammers.
II. Some hammers are boxes.
III. Some rings are boxes.

II is the converse of first premise and so it holds.

Some boxes are hammers. Some hammers are beads.

Since both the premises are particular, no definite conclusion can be drawn.

Some hammers are beads. All beads are rings.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some hammers are rings'. I is the converse of this conclusion and so it holds.

Some boxes are hammers. Some hammers are rings.

Since both the premises are particular, no definite conclusion can be drawn.