Please help the student to remember his long division homework?

Question

A student was assigned a long division homework which he was able to correctly work out. Unfortunately the dog ate his homework, and all that was left was what you see below. All the digits were smudged except for an '8'. Help the student to reconstruct his homework.

Each x stands for a digit (not necessarily unique). The dots are only to make the digits line up.

..................x x 8 x x
........___________
x x x | x x x x x x x x
.............x x x
..........._____
................x x x x
...................x x x
..............______
......................x x x x
......................x x x x
......................_______

Answer 1

I saw a similar problem to this once with NO digits given explicitly. I'll have to see if I can dig it up.

In any case, I won't attempt to reproduce my working here graphically because of the amount of time I'd have to spend making numbers line up. I'll note that immediately we can tell several things: three-digit numbers subtracted from four-digit numbers with a two-digit remainder mean the three-digit number must start with a 9 and the four-digit number must start with 1; there are some evident 0s in the quotient; the 8 in the quotient gives a three-digit product, so the divisor must start with a 1; since the last digit of the quotient gives a four-digit product (and the 8 gave a three-digit product) the last digit of the quotient must be 9. Note that already we know the quotient is of form x0809, and the divisor is between 112 and 124 (it must be greater than 1000/9 and less than 1000/8).

We also know the first digit of the quotient must multiply the divisor to give a number in the 900s. Now 7×124 = 868, so the quotient must be 80809.

We also now have from the first subtraction 1xxx - 9xx = 1x, where 9xx is 8 times the divisor. So 9xx must be at least 981. So the divisor must be at least 981/8 = 122.625, i.e. must be 123 or 124. In fact, though, we can skip this; the divisor must be at least 10000000/80809 = 123.75 (2 d.p.) and we know it's no more than 124, so the problem is

. . . . . . .80809
. . . ___________
124) 10020316
. . . . .992
. . . . .___
. . . . . .1003
. . . . . . .992
. . . . . . .____
. . . . . . . .1116
. . . . . . . .1116
. . . . . . . .____

Answer 2

pagal hai kya

Answer 3

nice problem .......i think DR D,now d student will finish his homework dis time......n do tell him that dis time he keep away notes from d dog.


.........80809
________________
124/10020316
.........992
________________
..........1003
............992
________________
..............1116
..............1116
________________
...............0000