NPR Sunday Puzzle (August 28) - Alaskan Conundrum

NPR Sunday Puzzle (August 28) - Alaskan Conundrum

Q: Take a two-word phrase meaning "a difficult puzzle." Drop the first letter, read the remaining letters backward, and you'll get a word for part of Alaska. What is it?

Again, I won't give the answer before the end of the puzzle period, but I will tell you that Alaska isn't the only place to have this 'part'. Work on this on your own and I'm sure you'll have it cracked before then.
Edit: Hopefully you caught all the hints given above... Here's my answer:

A: Difficult Puzzle: HARD NUT --> Part of Alaska: TUNDRA

NPR Sunday Puzzle (August 21) - Supermarket Brands

NPR Sunday Puzzle (August 21) - Supermarket Brands

Q: Name two familiar products you might find in a drug store or supermarket. These are well known national brands that compete with each other. Each name has five letters. Put them together, one after the other, and you'll get a well known geographical name, also five-five. What is it?

For some reason this answer came almost immediately. Could it be coincidental that Egypt is on the same continent?

A: IVORY COAST - Ivory and Coast are competing brands of soap (from Proctor & Gamble and Dial, respectively)

NPR Sunday Puzzle (August 7) - Three take away one leaves one

NPR Sunday Puzzle (August 7) - Three take away one leaves one

Q: Think of a word in three syllables starting with the letter 'A'. Remove the 'A' and you'll be left a new word and only one syllable. What is it? Here's a hint: The first word has three vowels, counting the A.

I actually have two answers for this one, but they only differ by one letter. It's not that difficult if you think of the first 'a' as one syllable and try and figure out how the remaining letters can both make two syllables and one syllable. I don't want to give away my answer(s) until after the Thursday deadline, so check back then...
Edit: As I said, I actually have two answers that work. Here they are:

A: AGAPE (love) --> GAPE (to open the mouth wide)
AGAVE (plants having spiny-margined leaves) --> GAVE (presented to another)