| The quotient is clearly 90809. We see that the 3-digit divisor xxx must
satisfy:
xxx >= 100
xxx * 8 < 1000
xxx * 9 >= 1000
so,
111 < xxx < 125.
We can easily test each of these divisors, checking that it satisfies:
10 <= [90809*xxx/10000] - 9*xxx <= 99
10 <= [90809*xxx/100] - 908*xxx <= 99
The only value of the divisor in the range that satisfies this is 124.
So, the solution is:
124 ) 11260316 ( 90809
1116
----
1003
992
----
1116
1116
----
|
|
Where two digits are brought down at one step, it is clear
that a zero occurs in the quotient.
So it is x080x.
Let us call the divisor D. Since 8D has but three digits,
the other two multiples of D which contain four digits, must
be each 9D,
so the quotient is 90809.
A tree digit number is less than 1000.
Hense 8D < 1000
and so D < 125.
A six digit number is greater than 99999 and when 9D is
subtracted from the dividend, a six digit number remains, and the
division comes out without remainder.
Hense 809D > 99999
and so 492
d > 123 ---
809.
It follows that D = 124.
We have the product 124 * 90809 = 11260316
so we reconstitute the division as follows:
124 ) 11260316 ( 90809
1116
----
1003
992
----
1116
1116
----
Enjoy,
Kostas G.
|