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There are two versions of the Fukuoka Tourist City Pass. From the official website:
- Fukuoka CityοΌnot applicable to Nishitetsu TrainοΌ: Adult 820 yen, Child 410 yen
- Fukuoka City and Dazaifu: Adult 1,340 yen, Child 670 yen
So the more expensive one will include the train to Dazaifu. This is also noted in the brochure with more details on what trains you can use: