A few years ago, my child brought a puzzle home from their 6th-grade math teacher. The solution was to use all the numbers $1−9$ only once and make the equation true. Using a spreadsheet, I was able to calculate the 2 answers: $631892754$ and $631472958$
My problem is I found the spreadsheet and the answers but I don’t remember the original problem. I have tried to recreate it using my spreadsheet formulas, but just not getting anywhere.
I think it was in a format similar to _ _ * _ _ * _ = _ _ ∗_ _ (each underscore a different number $1-9$) Might even have some parenthesizes. I don’t think it had any division, but I could be wrong. I am also fairly certain it was a single equation. I remember showing it to a co-worker the next day and I was able to write the question down from memory. It wasn’t overly complicated since I was able to figure out quickly what was required and it didn’t require any advanced math.
These are my formulas from the spreadsheet for the first solution $631892754$.
Step 1: Using all combinations of digits 1, 2, and 5.
Digit $1$ multiplied by digit $5$, divide by digit $2$. Result is digits $3$ and $4$.
Answer must be a whole number greater than 10, cannot end in 0.
Using the first answer $(6∗9)/3=18$
Step 2: Using the digits and the answers from Step 1.
Digit $5$ multiplied by digit $1$ must equal digits $3$ and $4$ multiplied by digit $2$
Using the first answer $9∗6=18∗3$
Step 3: I have 5 numbers, determine which numbers have not been used for each potential answer. Tried all combinations of the remaining 4 digits until I got the answer.
Digit $6$ and $7$ multiplied by digit $1$ must equal digits $8$ and $9$ multiplied by digit $2$
I spent a few hours searching the Internet for this puzzle, but no luck. I am hoping the above information is enough to go on.