The rightmost digit must be 1 or 3 or 6 or 8 which does not help. However, if the leftmost digit of N is a and 7>= a >=2, the leftmost digit of 6N will be one of the digits: 1, 2, 3, 4. Now assume that the leftmost digit of N is 8. Then 9 x 10^k > N >= 8 x 10^k for some non-negative integer k. Hence 54 x 10^k > 6N >= 48 x 10^k, and therefore either the leftmost digit of 6N or its second leftmost digit is one of the digits: 0, 1, 2, 3. So the leftmost digit of N is either 1 or 9. Hence the digit in question must be 9. solution {E}
由於6N的末位數不為0,1,2,3,4,故N的末位數必然是1,3,6,8,但此結論對解答並無助益。 考慮N的首位數a,當 7>= a >=2時,6N的首位數為1,2,3或4,不可能是綠色數。
當 a =8時,可知9 x 10^k > N >= 8 x 10^k,其中k為非負整數,則54 x 10^k >= 6N >= 48 x 10^k,由此可得6N的首位數是4或6N的首第二位數是0, 1, 2, 3,也不可能是綠色數。 所以N的首位數必須是1或9。例如13x6=78, 98x6=588. 故另外一個數是9,答案(E)
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