19. Using only the digits 1 through 9 one time each, is it possible to construct a 3 by 3 magic square with the digit 3 in the center square? That is, is it possible to construct a magic square of the form a b. e h where a, b, c, d, e. f, g,hare all distinct digits, none of which is equal to 3? Either construct such a magic square or prove that it is not possible. 13

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Chapter2: Second-order Linear Odes
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9.
10
19. Using only the digits 1 through 9 one time each, is it possible to construct a 3
by 3 magic square with the digit 3 in the center square? That is, is it possible
to construct a magic square of the form
a
d
3.
e
g
where a, b, c, d, e. f.g.hare all distinct digits, none of which is equal to 3?
Either construct such a magic square or prove that it is not possible.
20. Evaluation of proofs
See the instructions for Exercise (19) on page 100 from Section 3.1.
(a) Proposition. For each real number x, if x is irrational and m is an
integer, then mx is irrational.
Transcribed Image Text:9. 10 19. Using only the digits 1 through 9 one time each, is it possible to construct a 3 by 3 magic square with the digit 3 in the center square? That is, is it possible to construct a magic square of the form a d 3. e g where a, b, c, d, e. f.g.hare all distinct digits, none of which is equal to 3? Either construct such a magic square or prove that it is not possible. 20. Evaluation of proofs See the instructions for Exercise (19) on page 100 from Section 3.1. (a) Proposition. For each real number x, if x is irrational and m is an integer, then mx is irrational.
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