hash (v.)
1650s, "to hack, chop into small pieces," from French hacher "chop up," from Old French hache "ax" (see hatchet). Hash browns is short for hash browned potatoes (1917), with the -ed omitted, as in mash potatoes. The hash marks on a football field were so called 1960s, from similarity to hash marks, armed forces slang for "service stripes on the sleeve of a military uniform" (1909), which supposedly were called that because they mark the number of years one has had free food (hash (n.1)) from the Army; but perhaps there is a connection with the noun form of hatch (v.2).
hash (n.2)
short for hashish, 1959.
hash (n.1)
"a stew," 1660s, from hash (v.). Meaning "a mix, a mess" is from 1735.