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Someone recently told me to pour diesel fuel in the hole, because I
have rats in my barn, and can not use poison around livestock, and
have cats too. I have not tried it yet, but plan to.
Of course you could always catch it, put a modular plug on it's tail
and use it for a computer mouse
Is it a rat or a mouse?

It could be both. There are two cats that visit the rear of the shed
everyday that are not ours and I have placed a small mouse trap in
the area and caught nothing. The cats could be get hurt from the trap.

The rat or mouse moves so fast to see what it is and now has
dug up some soil. Some mice are showing up in our bed room
under the ground, we've caught a few mice. This is a house with a
concrete foundation slap. Don't know how they could chew thru
concrete.

Thanks to everyone for ideas.