AuD Problem

(1, 2, 5, 3, 4) ## ((1+2)*3)*(4+(5*7))
(1, 3, 5, 2, 4) ## 1+2*(3*4)+(5*7)
(1, 4, 2, 3, 5) ## 1+2*3*(4+5)*7
(1, 4, 2, 5, 3) ## 1+2*3*(4+5)*7)
(1, 4, 5, 2, 3) ## (1+2)*3*((4+5)*7)
(1, 5, 2, 3, 4) ## 1+(2*3)*4+(5*7)
(1, 5, 2, 4, 3) ## 1+2*3*(4+(5*7)))
(1, 5, 3, 2, 4) ## 1+2*(3*4+(5*7))
(1, 5, 3, 4, 2) ## 1+2*((3*4)+(5*7))
(1, 5, 4, 2, 3) ## 1+(2*3)*(4+(5*7))
(2, 1, 5, 3, 4) ## (1+(2*3))*4)+(5*7)
(2, 1, 5, 4, 3) ## (1+(2*3))*(4+(5*7)))
(2, 3, 5, 1, 4) ## 1+((2*3)*4)+5*7
(2, 4, 1, 3, 5) ## (1+(2*3))*((4+5))*7)
(2, 4, 1, 5, 3) ## (1+(2*3))*((4+5))*7)
(2, 4, 5, 1, 3) ## 1+(2*3)*((4+5)*7)
(2, 5, 1, 4, 3) ## 1+(2*3)*(4+(5*7)))
(2, 5, 1, 3, 4) ## (1+(2*3))*4)+(5*7)
(2, 5, 3, 1, 4) ## 1+(2*3)*4+(5*7)
(2, 5, 3, 4, 1) ## 1+(2*3)*4)+(5*7)
(2, 5, 4, 1, 3) ## (1+(2*3))*(4+(5*7)))
(2, 5, 4, 3, 1) ## (1+(2*3))*(4+(5*7)))
(3, 1, 2, 4, 5) ## (1+2)*((3*4)+5)*7
(3, 1, 2, 5, 4) ## (1+2)*((3*4)+(5*7))
(3, 1, 4, 2, 5) ## ((1+2)*(((3*4))+5)*7)
(3, 1, 4, 5, 2) ## ((1+2)*((3*4))+5)*7
(3, 1, 5, 2, 4) ## ((1+2)*((3*4))+(5*7))
(3, 1, 5, 4, 2) ## ((1+2)*((3*4))+(5*7))
(3, 2, 1, 4, 5) ## (1+(2*((3*4)+5)*7
(3, 2, 1, 5, 4) ## (1+(2*((3*4)+(5*7))
(3, 2, 5, 1, 4) ## (1+(2*((3*4)+(5*7))
(3, 2, 5, 4, 1) ## 1+(2*(3*4))+5*7
(3, 4, 1, 2, 5) ## (1+2)*(3*4)+(5*7)
(3, 4, 1, 5, 2) ## ((1+2)*(3*4))+(5*7)
(3, 4, 2, 5, 1) ## (1+(2*(3*4)+(5*7)
(3, 4, 5, 1, 2) ## (1+2)*(3*4)+5*7
(3, 5, 1, 2, 4) ## (1+2)*((3*4)+(5*7))
(3, 5, 1, 4, 2) ## ((1+2)*((3*4))+(5*7))
(4, 1, 2, 3, 5) ## (1+2)*3*((4+5)*7)
(4, 1, 2, 5, 3) ## (1+2)*(3*((4+5))*7)
(4, 1, 3, 2, 5) ## ((1+2)*(3*((4+5)))*7)
(4, 1, 3, 5, 2) ## ((1+2)*(3*((4+5)))*7)
(4, 1, 5, 2, 3) ## ((1+2)*3)*((4+5)*7)
(4, 1, 5, 3, 2) ## ((1+2)*(3*((4+5)))*7)
(3, 5, 2, 1, 4) ## (1+(2*((3*4)+(5*7))
(3, 5, 2, 4, 1) ## (1+(2*((3*4)+(5*7))
(3, 5, 4, 1, 2) ## (1+2)*((3*4)+(5*7))
(3, 5, 4, 2, 1) ## (1+(2*((3*4)+(5*7))
(5, 1, 2, 3, 4) ## (1+2)*3*4+(5*7)
(5, 1, 2, 4, 3) ## (1+2)*(3*(4+(5*7)))
(5, 1, 3, 2, 4) ## ((1+2)*((3*4))+(5*7))
(5, 1, 3, 4, 2) ## ((1+2)*(3*4))+(5*7)
(5, 1, 4, 2, 3) ## ((1+2)*3)*(4+(5*7))
(5, 1, 4, 3, 2) ## ((1+2)*(3*(4+(5*7))))
(4, 2, 1, 5, 3) ## 1+(2*3)*(4+5)*7
(4, 2, 3, 1, 5) ## (1+(2*3))*((4+5)*7)
(4, 2, 3, 5, 1) ## (1+(2*3))*((4+5)*7)
(4, 2, 5, 1, 3) ## (1+(2*3))*((4+5))*7)
(4, 2, 5, 3, 1) ## (1+(2*3))*((4+5))*7)
(4, 3, 1, 2, 5) ## (1+2)*(3*(4+5))*7
(4, 3, 1, 5, 2) ## ((1+2)*(3*((4+5)))*7)
(4, 3, 5, 1, 2) ## 1+2*((3*(4+5))*7)
(4, 5, 1, 2, 3) ## 1+2*3*((4+5)*7)
(4, 5, 1, 3, 2) ## ((1+2)*(3*(4+5)))*7
(4, 5, 2, 1, 3) ## 1+((2*3)*((4+5)*7))
(4, 5, 2, 3, 1) ## (1+(2*3))*(4+5)*7
(4, 5, 3, 1, 2) ## (1+2)*(3*(4+5))*7
(5, 2, 1, 3, 4) ## (1+(2*3))*4)+(5*7)
(5, 2, 1, 4, 3) ## (1+(2*3))*(4+(5*7)))
(5, 2, 3, 1, 4) ## (1+(2*3))*(4+(5*7))
(5, 2, 3, 4, 1) ## (1+(2*3))*4+(5*7)
(5, 2, 4, 1, 3) ## (1+(2*3))*(4+(5*7)))
(5, 2, 4, 3, 1) ## (1+(2*3))*(4+(5*7)))
(5, 3, 1, 2, 4) ## (1+2)*(3*4)+(5*7)
(5, 3, 1, 4, 2) ## ((1+2)*((3*4))+(5*7))
(5, 3, 2, 1, 4) ## (1+(2*(3*4))+(5*7)
(5, 3, 2, 4, 1) ## (1+(2*((3*4)+(5*7))
(5, 3, 4, 1, 2) ## (1+2)*(3*4)+(5*7)
(5, 3, 4, 2, 1) ## (1+(2*(3*4)+(5*7)
(5, 4, 1, 2, 3) ## (1+2)*3*(4+(5*7))
(5, 4, 1, 3, 2) ## ((1+2)*(3*(4+(5*7))))
(5, 4, 2, 1, 3) ## 1+(2*3)*(4+(5*7))
(5, 4, 2, 3, 1) ## 1+(2*3)*(4+(5*7))
(5, 4, 3, 1, 2) ## (1+2)*(3*(4+(5*7)))





(1, 2, 3, 4, 5) ## 1+2*3*4+5*7
(1, 2, 3, 5, 4) ## 1+2*3*4+(5*7)
(1, 2, 4, 3, 5) ## 1+2*3*(4+5)*7
(1, 2, 4, 5, 3) ## 1+2*3*((4+5)*7)
(1, 2, 5, 4, 3) ## 1+2*3*(4+(5*7)))
(1, 3, 2, 4, 5) ## 1+2*(3*4)+5*7
(1, 3, 2, 5, 4) ## 1+2*(3*4)+(5*7)
(1, 3, 4, 2, 5) ## 1+2*((3*4)+5)*7
(1, 3, 4, 5, 2) ## 1+2*(((3*4)+5)*7)
(1, 3, 5, 4, 2) ## 1+2*((3*4)+(5*7))
(1, 4, 3, 2, 5) ## 1+2*(3*(4+5))*7
(1, 4, 3, 5, 2) ## 1+2*((3*(4+5))*7)
(1, 4, 5, 3, 2) ## 1+2*(3*((4+5)*7))
(1, 5, 4, 3, 2) ## 1+2*(3*(4+(5*7)))
14
(2, 1, 3, 4, 5) ## (1+(2*3))*4)+5*7
(2, 1, 3, 5, 4) ## (1+(2*3))*4+(5*7)
(2, 1, 4, 3, 5) ## (1+(2*3))*(4+5)*7
(2, 1, 4, 5, 3) ## (1+(2*3))*((4+5)*7)
(2, 3, 1, 4, 5) ## 1+((2*3)*4)+5*7
(2, 3, 1, 5, 4) ## 1+((2*3)*4)+(5*7)
(2, 3, 4, 1, 5) ## 1+(((2*3)*4)+5)*7
(2, 3, 4, 5, 1) ## 1+((((2*3)*4)+5)*7)
(2, 3, 5, 4, 1) ## 1+(((2*3)*4)+(5*7))
(2, 4, 3, 1, 5) ## (1+((2*3)*(4+5)))*7
(2, 4, 3, 5, 1) ## 1+((2*3)*(4+5)*7)
(2, 4, 5, 3, 1) ## 1+((2*3)*((4+5)*7))
12
(3, 2, 4, 1, 5) ## 1+((2*(3*4))+5)*7
(3, 2, 4, 5, 1) ## 1+(((2*(3*4))+5)*7)
(3, 4, 2, 1, 5) ## 1+(2*((3*4)+5))*7
(3, 4, 5, 2, 1) ## 1+(2*(((3*4)+5)*7))
4
(4, 2, 1, 3, 5) ## 1+(2*3)*(4+5)*7
(4, 3, 2, 1, 5) ## (1+(2*(3*(4+5))))*7
(4, 3, 2, 5, 1) ## 1+((2*(3*(4+5))))*7)
(4, 3, 5, 2, 1) ## 1+(2*((3*(4+5))*7))
(4, 5, 3, 2, 1) ## (1+(2*(3*((4+5)*7)))
6
(5, 4, 3, 2, 1) ## (1+(2*(3*(4+(5*7)
1
--
37 Möglichkeiten


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Abhängigkeiten:
5<4<3<2<1
  4<3<2<1
    3<2<1
      2<1
        1

1 unabhängig 	=> 4!=24 Möglichkeiten
	2 abhängig	=> 4!-3!=18
		3 abhängig   => 2
		3 unabhängig => 2
1  abhängig	=> 5! -4!=96 Möglichkeiten
	2 unabhängig	=> 6
		3 unabhängig => 2
		3 abhängig   => 2
12 unabhängig	=> 3!=6 Möglichkeiten
	3 abhängig	=> 2
12 abhängig	=> 4! -3!=18
	3 unabhängig	=> 2
123 unabhängig	=> 2! Möglichkeiten
	4 abhängig	=> 1
123 abhängig	=> 3! -2!=4
	4 unabhängig	=> 2
1234unabhängig	=> 1  Möglichkeit
1234abhängig	=> 2
	5 abhängig	=> 1
	5 unabhängig	=> 1


1+2*3*4+5*7