An anti magic square is an N×N
grid containing the integers from
1 through N^2, such that the sum of
each row, column, and main diagonal
is a different number, and those
sums form a consecutive sequence of
integers.
There are no 3×3 anti magic squares, but there are some that are close in that the sequence of sums is consecutive except for one missing value.
Determine a 3×3 near anti magic square in which the three digit number represented by the top left (hundreds position) to bottom right (units position) main diagonal is a minimum. Present your answer as a 3×3 grid containing the digits 1 through 9.
Call a fraction a "unit fraction" if it can be written as 1/n, where n is a positive integer.
How many more ways can the unit fraction 1/n be written as a sum of two (possibly equivalent) unit fractions than as a difference of two unit fractions?
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