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Tickets available in the internet:
Milano Centrale - Bern: 68 EUR
Milano Centrale - Lausanne: 65 EUR
Milano Centrale - Brig: 34 EUR

Timetables:
Milano C dp.. 8.25, 12.25, 17.25,
Lausanne ar 11.40, 15.40, 20.40,
Lausanne dp 11.45, 15.45,20.45, change at Neuchatel, Fare 33 CHF
La Chx-d-Fds12.59, 16.59, 21.59,

Milano Centr dp 07.25, 11.25, 18.25
Bern ar..............10.23, 14.23, 21.23
Bern dp.............10.53, 14.53, 21.34 change at Neuchatel, Fare 26 CHF
La Chx-d-Fds ar 11.59, 15.59, 23.13

If you travel via Lausanne, you can buy your Lausanne - La Chaux de Fonds ticket in the train between Domodossola and Lausanne, but you will have to pay a surcharge. In order to avoid that, you can buy your ticket at Lausanne (counter or ticket machine, CHF or credit card only) and leave Lausanne 1 hour later or you can try to buy a mobile ticket before you leave Milan: http://www.sbb.ch/en/travelcards-and-tickets/e-tickets/mobileticket.html

If you travel via Bern, you will have enough time fo buying your onward ticket there (counter or ticket machine, CHF or credit card only).

You may also buy a internet ticket up to Brig only and buy your Swiss ticket there (counter or ticket machine, CHF or credit card only). Trains vrom Brig to Bern every hour from 6.49 until 19.49, connecting trains from Bern to Biel/Bienne and then to la Chaux de Fonds.

All ticket counters will be closed in late evening.

Seat reservation is not compulsory (and not usual) for travel within Switzerland.