Hi there!
Hmm - I see the problem - you need a 18 day rail pass :) !
Lets look at your costs:
- Narita airport terminal 1 > Tokyo: ¥2740, (62mins, 79km)
- Tokyo > Hiroshima: ¥17850, (291mins, 894km)
- Hiroshima > Osaka: ¥10220, (109mins, 345km)
- Osaka > Nagoya: ¥5980, (66mins, 190km)
- Nagoya > Kyoto: ¥5240, (37mins, 147km)
- Kyoto > Tokyo: ¥13020, (161mins, 513km)
- Tokyo > Nagano: ¥7770, (105mins, 222km)
- Nagano > Odawara: ¥11120, (155mins, 306km)
- Odawara > Tokyo: ¥1450, (36mins, 83km)
- Tokyo > Narita airport terminal 1: ¥2740, (58mins, 79km)
TOTAL: ¥78,130 for 11 legs
This means that even if you got a 21 day pass, you'll save ¥20,430. The question is: "can you save more"?
Well... Firstly, the difference between a 21 day and a 14 day is ¥12,600 (¥57700-¥45100), so you will need to spend at least that on individual tickets for a 21 day rail pass to be worth it over a 14 day.
Lets try and compress your most expensive days into a 14 day pass covering the 9-23:
- Tokyo > Hiroshima: ¥17850, (291mins, 894km)
- Hiroshima > Osaka: ¥10220, (109mins, 345km)
- Osaka > Nagoya: ¥5980, (66mins, 190km)
- Nagoya > Kyoto: ¥5240, (37mins, 147km)
- Kyoto > Tokyo: ¥13020, (161mins, 513km)
- Tokyo > Nagano: ¥7770, (105mins, 222km)
- Nagano > Odawara: ¥11120, (155mins, 306km)
TOTAL: ¥71,200 for 8 legs
It looks like with a 14 day pass, your savings are even greater than with a 21 day! ¥6930 in tickets + ¥45,100 14 day rail pass = ¥52,030, saving you a total of ¥26,100 on the actual ticket costs and ¥5670 over a 21 day rail pass.
So in your case, the 14 day JR Pass + individual tickets looks like the best way to go. Of course, you loose flexibility on the ticket days, but it is certainly the most financially efficient.
Hope this helps!