T.M.
Hi T.,
I teach 8th grade science and we do a unit on stains and solvents. Most permanent markers are alcohol based instead of water based and so people often have luck removing them with rubbing alcohol. If you can find an isopropyl (rubbing) alcohol that is 99% instead of in the 70% range the 99% works best but it is hard to find in drug stores. I would definitely use rubbing alcohol on the linoleum. The ink should come right off. As for the carpet, you can try the rubbing alcohol too, but just know that it causes the ink to run a bit. You are going to want to have several clean rags on hand to dab up and the rubbing alcohol may dilute the stain and cause it to spread before it is removed. It may take quite a bit of rubbing alcohol to do the trick. The same thing happens on clothing. The ink will run with the rubbing alcohol so you definitely want to be ready to soak it up with something. Rubbing alcohol is also a bit stinky, so you will want to keep the room well ventilated. I would let that evaporate away and then follow up with a good carpet cleaner. I have had great luck with "Kids and Pets" stain remover. You will probably want to let most of the alcohol evaporate away first though.
The hair spray trick that someone else mentioned can work also, but mostly because most hairsprays have alcohol in them. Aqua Net has a ton of alcohol and I have found it works well for ink stains on clothing, but have never tried it on carpet.
I hope this helps. Good luck!