For any positive integer N, consider the digits which occur either in N or in 7 x N. Let m be the smallest digit among those digits. What is the largest possible value of m ?
2007-08-03 17:04:52 · 3 answers · asked by The Questionneur 1 in Science & Mathematics ➔ Mathematics
The largest value that m can have is 6.
I cannot prove this, but consider the following argument:
If n begins with a 7 and has only digits that are 7, 8, or 9, then 7*n begins with 54 or 55. 4 and 5 are lower than 6.
If n begins with an 8 and has only digits that are 7, 8, or 9, then 7*n begins with 61 or 62. 1 and 2 are lower than 6.
If n begins with a 9 and has only digits that are 7, 8, or 9, then 7*n begins with 68 or 69.
The largest value the smallest digit out of both numbers can have is 6.
2007-08-03 17:16:48 · answer #1 · answered by lithiumdeuteride 7 · 0⤊ 0⤋
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2007-08-04 00:11:42 · answer #2 · answered by Earendil 2 · 0⤊ 0⤋
6. 7 * 97 = 679
2007-08-04 00:16:14 · answer #3 · answered by Mike S 3 · 0⤊ 0⤋