AMC 8 2001 Problem 4
AMC8 2001 年第 4 题
奇偶性★★☆☆☆
The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible even five-digit number. The digit in the tens place is
数字 1，2，3，4 和 9 每个使用一次，形成最小的五位偶数。则这个数的十位数字是？
- A.1
- B.2
- C.3
- D.4
- E.9
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
Since the number is even, the last digit must be 2 or 4. To make the smallest possible number, the ten-thousands digit must be as small as possible, so the ten-thousands digit is 1. Simillarly, the thousands digit has second priority, so it must also be as small as possible once the ten-thousands digit is decided, so the thousands digit is 2. Similarly, the hundreds digit needs to be the next smallest number, so it is 3. However, for the tens digit, we can't use 4, since we already used 2 and the number must be even, so the units digit must be 4 and the tens digit is 9, (The number is 12394.) We know that the smallest possible number is 12349. However, 12349 is an odd number. Thus, by shifting the 4 (the largest even number) into the unit's place and rearranging the rest of the digits from least to greatest, we arrive at 12394. Thus, the digit in the tens place is 9.
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