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Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. Two solutions are considered to be the same if, as in the example shown, they contain the same six triples. How many different solutions can you find?
Show that it is impossible to place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that the diagonals, as well as all the rows and columns, add up to prime numbers.