Calculation of the determinants + verifiation

1.

Calculation of the determinants + verifiation
a11
a12
a13
a21
a22
a23 a11a22 a33 a12 a23 a31 a12 a32 a13 a31a22 a13 a21a12 a33 a11a32 a23
a31
a32
a33
n
det A aik ( 1)i k det A(i ,k )
k 1
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2.

Dodgson condensation
Charles Lutwidge Dodgson
(better known as Lewis Carroll)
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3.

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5.

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7.

Сonstructive problems on divisibility
1. How many zeros ends the number 100!
2. How many six-digit numbers exist in which all digits are odd?
3. How many six-digit numbers exist that have at least one even
digit in the record?
4. Can the sum of 19 consecutive positive integers be divisible by
87?
5. Can the sum of 12 consecutive positive integers be divisible by 4?
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