The third badge is in Goldenrod City.
The badge from Cianwood.
The 7th badge is in mahogany town.
if you are looking for the third gym badge i suggest Veilstone city.
To use cut outside of battle in Pokemon gold version you need the second badge from Azalea Town from the gym leader Bugsy.
You get your 3rd badge in Veilstone city against Maylene.
In gym number seven
you got to go to veilstone and that's where she is.
it's the 3rd badge!
go to kanto and beat lt surge
you have to beat blaze then you can go ther
Directly to the right of the city with the fourth badge.
you go to ecruteak city