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X and Lucky Seven Settlement (Posted on 2022-06-18) Difficulty: 3 of 5
         x 7 x
   ____________
x x) x x x x x
     x 7 7
    ----------
       x 7 x
       x 7 x
     ---------
           x x                            
           x x                                 
          ----- 
In this skeletal division problem:
  • Each of the x's denote a digit from 0 to 9, whether same or different.
  • None of the x's denote the digit 7
  • None of the numbers can contain a leading zero.
Complete the above-mentioned division.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 3
There are only two options for the first digit of the quotient and for the 2-digit divisor to get x * xx = x77 and they are:
3 * 59 = 177.
9 * 53 = 477

Moreover, the 3rd digit of the dividend must be 4 in order to be able to subtract xxx minus x77 and get x7x

So there are only 18 possibilities (x cannot be 7) for (divisor, quotient) pairs
59 * 37x and 53 * 97x

Only two of these put a 4 as the third digit of the dividend:
53 * 970 = 51410
53 * 971 = 51463

We can fill in quite a bit of the grid now

         9 7 x
   ____________
5 3) 5 1 4 x x
     4 7 7
    ----------
       3 7 y
       3 7 1
     ---------
           x x                            
           x x                                 
          ----- 

And the 4th digit of the dividend (51410 or 51463) could be 1 or 6, but if it's a 1 (see "y") then the second from bottom 2 digit number would have a leading zero.

         9 7 1
   ____________
5 3) 5 1 4 6 3
     4 7 7
    ----------
       3 7 6
       3 7 1
     ---------
           5 3                            
           5 3                                 
          ----- 

  Posted by Larry on 2022-06-18 09:29:31
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