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None of them is "wrong", nor really "different" in meaning, but 1(c) and 2(a) are the preferred expressions (in AmE).
I can't explain why. But here is some confirmation.
https://books.google.com/ngrams/graph?content=opened+the+book+at+%C2%A0page%2C+opened+the+book+on+page%2C+opened+the+book+to+page&case_insensitive=on&year_start=1800&year_end=2000&corpus=17&smoothing=3&share=&direct_url=t1%3B%2Copened%20the%20book%20at%20page%3B%2Cc0%3B.t1%3B%2Copened%20the%20book%20to%20page%3B%2Cc0
https://books.google.com/ngrams/graph?content=book+fell+open+at%2C+book+fell+open+on%2Cbook+fell+open+to&case_insensitive=on&year_start=1800&year_end=2000&corpus=18&smoothing=3&share=&direct_url=t1%3B%2Cbook%20fell%20open%20at%3B%2Cc0
None of them is "wrong", nor really "different" in meaning, but 1(c) and 2(a) are the preferred colloquial expressions (in AmE).
None of them is "wrong", nor really "different" in meaning, but 1(c) and 2(a) are the preferred colloquial expressions (in AmE). I can't explain why.
