Knowledge You Can Build On — Est. 1998
Friday puzzle -- long division
The following problem is a traditional long division problem in which all of the digits except for the answer have been replaced by Xs, and the answer is missing except for one digit in the correct spot. Replace the Xs and fill in the answer.
recuse myself
I will abstain on this one. I have used this one before in the math lab I was tutoring in and have the answers.
Re: recuse myself
According to Martin Gardner, this is the most popular puzzle ever published in The American Mathematical Monthly, having appeared in the April, 1954 issue. It is much easier than it looks, so I will add a hint to get folks started on this one.
Hint
This puzzle looks intimidating, but yields to pretty straight-forward reasoning. To start, note that when 8 is multiplied by the three-digit divisor, the result has three digits. That limits the size of the divisor. Note also that before and after the 8, two digits are brought down, which happens if and only if the quotient is zero in those spaces. Next, it should be easy to see what the last digit in the quotient is.
Keep making observations like that, and you will have the complete solution (not just the quotient) in short order.
Re: Hint
I looked at this when first posted and mis-read the directions; I thought the dividend began with 8 (the 8 shown) and could not see how to proceed.
With the hint, and having re-read the directions, I think I see at least one answer - the quotient is 80809. Are there more possibilities?
1/2-way there
Yes, good job; 80809 is the quotient. Continuing the process, it is possible to fill in all the Xes.
Sorry if the instructions were not clear.
Here you go
......___80809
124)10020316
........992
.........1003
...........992
............1116
............1116
:-)
