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In how many positive four-digit integers that are not multiples of 1111 do the digits form a geometric sequence? (The digits must form a geometric sequence, in order. For example, the number 8412 does not count.)

 Sep 4, 2021
 #1
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There are 8 numbers that work.

 Sep 4, 2021
 #2
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The sequence 1248 is geometric with a common ratio of 2.

The sequence 8421 is geometric with a common ratio of 1/2.

Each of the following are geometric, with a common ratio of 0:

      1000     2000     3000     4000     5000     6000     7000     8000     9000.

 Sep 4, 2021

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