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How many of the natural numbers from 1 to 800, inclusive, contain the digit 6 at least twice? (The numbers 266 and 663 are two natural numbers that contain the digit 6 at least twice, but 430 or 16 are not.)

 Apr 17, 2020
 #1
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The 6s could be in positions 2 and 3:  066, 166, 266, 366, 466, 566, 666, 766

The 6s could be in positions 1 and 3:  606, 616, 626, 636, 646, 666, 676, 686, 696

The 6s could be in positions 1 and 2:  660, 661, 662, 663, 664, 665, 666, 667, 668, 669

 

Count them (just don't count repeats) and make certain that I didn't forget any ...

 Apr 17, 2020
 #2
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66 , 166 , 266 , 366 , 466 , 566 , 606 , 616 , 626 , 636 , 646 , 656 , 660 , 661 , 662 , 663 , 664 , 665 , 666 , 667 , 668 , 669 , 676 , 686 , 696 , 766 , Total = 26

 Apr 17, 2020

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