AMC 8 2023 Problem 6
AMC8 2023 年第 6 题
表达式与运算★★☆☆☆
The digits 2, 0, 2, and 3 are placed in the expression below, one digit per box. What is the maximum possible value of the expression?
将数字2，0，2，3填入下面的表达式中，每个方框内填一个数字．问表达式的最大可能值是多少?
- A.0
- B.8
- C.9
- D.16
- E.18
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
First, let us consider the case where 0 is a base: This would result in the entire expression being 0. Contrastingly, if 0 is an exponent, we will get a value greater than 0. is greater than and Therefore, the answer is 9.
The maximum possible value of using the digits 2,0,2, and 3: We can maximize our value by keeping the 3 and 2 together in one power (the biggest with the biggest and the smallest with the smallest). This shows (We don't want because that is 0.) It is going to be 9.
Trying all 12 distinct orderings, we see that the only possible values are 0,4,8, and 9, the greatest of which is 9.
There are two 2's and one 3. To make use of them all, use 2 and 3 as the bases and 2 and 0 as the exponents..
If 0 is a base, then the whole expression becomes 0. Therefore, 0 must be an exponent. But since = = 1, we do not want to waste our 3 on the 0. We will have a 3 and a 2 left, and since is greater than , we get = 9.
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