AMC8 1993

AMC8 1993 · Q9

AMC8 1993 · Q9. It mainly tests Logic puzzles.

Consider the operation * defined by the following table: [table: 1*1=2,1*2=4,1*3=1,1*4=3; 2*?= table incomplete but from text; example 3*2=1]. Then (2 * 4) * (1 * 3) =

考虑由下表定义的操作 *：[表格：1*1=2,1*2=4,1*3=1,1*4=3; 2*?=表格不完整但从文本；例如3*2=1]。那么 (2 * 4) * (1 * 3) =

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (D)

正确答案：（D）

Solution

Substituting the values from the table yields \[(2\ast4)\ast(1\ast3)=3\ast3=4.\] Query. Would evaluating the products \[((2\ast4)\ast1)\ast3,\ (2\ast(4\ast1))\ast3,\ 2\ast((4\ast1)\ast3)\text{ and }2\ast(4\ast(1\ast3)),\] yield the same result?

把表中的取值代入： \[(2\ast4)\ast(1\ast3)=3\ast3=4.\] 问题：计算 \[((2\ast4)\ast1)\ast3,\ (2\ast(4\ast1))\ast3,\ 2\ast((4\ast1)\ast3)\text{ 与 }2\ast(4\ast(1\ast3))\] 会得到相同结果吗？

Topics

LM.001 Logic puzzles