part2 - Homewrok set # 1 solution posted on 9/11/02 Problem...

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Homewrok set # 1 solution posted on 9/11/02 Problem 1) Take } 5 , 4 , 3 , 2 , 1 , 0 { = A a) } 5 , , , / ) , , {( = + + = z y x A z A y A x z y x S 2) [GAR] 2.3 a) } 12 , 11 , 10 , 9 , 8 , 7 , 6 , 5 , 4 , 3 , 2 { = S b) } 12 , 10 , 8 , 6 , 4 , 2 { = A c) if )} 1 , 1 {( 2 = = S sum )} 1 , 2 ( ), 2 , 1 {( 3 = = S sum In general for 1 min(6, 1) (1, 6) {( , )} k Max k sum k S j k j =⇒= 12 k For example if )} 2 , 6 ( ), 3 , 5 ( ), 4 , 4 ( ), 5 , 3 ( ), 6 , 2 {( 8 = = S sum *Lower bound starts from 2 *Upper bound goes to 6 3) [GAR] 2.7 a) )} 1 , 2 , 3 ( ), 1 , 3 , 2 ( ), 2 , 3 , 1 ( ), 2 , 1 , 3 ( ), 3 , 1 , 2 ( ), 3 , 2 , 1 {( = S b) )} 2 , 3 , 1 ( ), 3 , 2 , 1 {( 1 = A )} 1 , 2 , 3 ( ), 3 , 2 , 1 {( 2 = A )} 3 , 1 , 2 ( ), 3 , 2 , 1 {( 3 = A c) )} 3 , 2 , 1 {( 3 2 1 = A A A The number of every ball corresponds to the number of the draw.
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