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