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The possible train solutions can be found in the Trenitalia site.
Currently the cheapest train from Milan to Ventimiglia is the regional train. It takes almost five hours and costs 22.25 euros.
It is possible, anyway, to find some good offers for faster trains at a price lower than the one of the regional train. These discounted seats have some limitations, for example you won't be able to change your reservation without paying an extra fee.
Upvote:4
Late to the game, but if it can help somene...
You can find rails tickets from Milano to Monaco on Thello
In 2017, price is 15β¬ if you book your ticket 1 month (or more) in advance.
But if you need it for tomorrow, the cost may go up to 42β¬.
There are 3 trains per day, usually 7AM, 11AM and 3PM. The journey takes approximatively 4h30.