The OP's usage of "cleave" is grammatically wrong. An intransitive verb does not take a direct object.
That is, when using this definition, the verb always operates on its subject alone. If you are the subject, you are doing the cleaving, which means you yourself are sticking. A prepositional phrase can specify the thing to which you are stuck, or modify how you are sticking, but that requires a preposition. You can "cleave to X" or perhaps "cleave on X", but you cannot simply "cleave X" unless you mean to split X apart.
To make this more clear, compare it to "thrive," another intransitive verb. A plant can thrive, or it can thrive on the windowsill, but it is nonsensical to say that you are "thriving the plant" or that the plant is "thriving the windowsill."
In your riddle, "cleave" has a direct object (one of the stones), which means you're using it as a transitive verb. The transitive form always has the meaning of "to split apart," never the connotation you're trying to arrive at. So the riddle just doesn't work.
That is, when using this definition, the verb always operates on its subject alone. If you are the subject, you are doing the cleaving, which means you yourself are sticking. A prepositional phrase can specify the thing to which you are stuck, or modify how you are sticking, but that requires a preposition. You can "cleave to X" or perhaps "cleave on X", but you cannot simply "cleave X" unless you mean to split X apart.
To make this more clear, compare it to "thrive," another intransitive verb. A plant can thrive, or it can thrive on the windowsill, but it is nonsensical to say that you are "thriving the plant" or that the plant is "thriving the windowsill."
In your riddle, "cleave" has a direct object (one of the stones), which means you're using it as a transitive verb. The transitive form always has the meaning of "to split apart," never the connotation you're trying to arrive at. So the riddle just doesn't work.