I live in an old house. I am changing the old honeywell thermostat to a new programmable one. When I took it off the wall it only had 2 wires. A white wire which is a W and a red wire which is a R. On the old model it had a little short red wire which should be a Y going to a 1. It didn't come from the wall wires. Just a single wire that was connected to the Y and the 1 spot. Any ideas what I need to do? Thanks.

Having only red & white wires connected to R&W terminals, it seems you only have heat & no A/C connected to the thermostat. Is that correct? If so, connect the red to R & white to W on the new stat. Don't be concerned about the other wire.