题目
A keypad is a 3 by 3 grid with the digits 1 to 3 in order on the top row,4 to 6 in order on the second row and 7 to 9 in order on the third row. Seb has the keypad upside-down (i.e rotated through 180°)and types his three-digit PIN as if the keypad were the right way up.The number he types in turns out to be k times his original PIN where k is a positive integer. Find all possible PINs and prove there are noothers. 一个3×3的网格键盘，第一行依次是数字1到3，第二行依次是数字4到6，第三行依次是数字7到9。Seb将键盘倒置(即旋转180°)，并按照键盘正常放置的方式输入他的三位数PIN码。结果他输入的数字是他原始PIN码的k倍，其中k是一个正整数。求所有可能的PIN码，并证明没有其他可能的PIN码。 ——CMO、数学表达、、〚CMO-2025.5〛
解答
解析 - 数学表达
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