I created a puzzle that I was curious what its properties are, and how it could be determined it is solvable or not. It consists of 6 rows of 3 of the same numbers, which in each row in order are 1, 2, 3, 4, 6, and 8.
1 1 1
2 2 2
3 3 3
4 4 4
6 6 6
8 8 8
The goal is to come up with 6 single digit multiplication equations (with only 3 numbers so not $2∗2∗2=8$) that allow no numbers to be left on the grid. An example equation could be $2∗3=6$ in which case you would cross off the 2, 3, and 6.
1 1 1
/ 2 2
/ 3 3
4 4 4
/ 6 6
8 8 8
Continuing making equations and crossing off numbers, is it possible to have all numbers crossed off? How would you figure that out and what about a grid with numbers that go higher than 8? I've been able to be left with only 3 numbers, and I have been able to solve a variant without the 3 8s at the end.