# In how many positive four-digit integers that are not multiples of 1111 do the digits form an arithmetic sequence? (The digits must form an arithmetic sequence, in order. For example, the number 5137 does not count.)

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1. so, start with 1xxx. With various values of d, we get
d=1: 1234, 2345, 3456, 4567, 5678, 6789
d=2: 1357, 2468, 3579
d=3: 147? bzzt

Now, with negative d, we have
d=-1: 9876, 8765, 7654, 6543, 5432, 4321, 3210
d=-2: 9753, 8642, 7531, 6420
d=-3: 9630

So, of the numbers listed, how many are not multiples of 1111?

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2. 6+7+4+1+3=21

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3. STEVE YOU MSUT HAVE FOR BRAINS!

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4. Agree that the answer is 21

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5. Yes, I checked. The answer is 21.

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