<PRE><B>Question 1210205</B>
&lt;br&gt;
At least 6 times means either all seven digits are the same or six of the seven are the same.&lt;br&gt;
(1) all 7 digits the same&lt;br&gt;
The digit can be any one of the 10 digits 0 to 9: 10 choices.&lt;br&gt;
There are 10 7-digit sequences containing a single digit 7 times.&lt;br&gt;
(2) 6 of the 7 digits the same&lt;br&gt;
(a) choose 1 of the 10 digits to be the one that occurs 6 times: 10 choices
(b) choose 1 of the other 9 digits to be the digit that is difference: 9 choices
(c) find the number of arrangements of the string AAAAAAB.  That number is&lt;br&gt;
{{{7!/((6!)(1!))=7}}}&lt;br&gt;
There are 7 ways to arrange those digits.&lt;br&gt;
Total number of 7-digit numbers with 6 of the digits the same: 10*9*7 = 630.&lt;br&gt;
Total number of 7-digit numbers with at least 6 digits the same: 10+630 = 640.&lt;br&gt;
ANSWER: 640&lt;br&gt;
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