100 Floors - Level 97

Completed early by request - thanks for your comment!

A door with four changeable numbers in front of it and lots of little lines and dots on it. A balloon hovers in front of it, and there are some numbers on the wall. Using your knife on the balloon gets you a clue, but what to do with the numbers after that? It's like being back in math class...

This is another math one, which are never the most intuitive ones for me. Once you have the scrap of paper, there are two sets of numbers on the wall: (30,235) and (735,____) where the ____ represents an empty space.

The first set is actually an equation: 30 = 2 x 3 x 5. So we are looking for something that equals 735, and we know it will have four numbers because of the four numbers in front of the door. Call the numbers A, B, C and D for now: 735=AxBxCxD.

735 ends in 5 so chances are one of the numbers we will need is a 5. So we have 735=5xBxCxD, or 147=BxCxD. 147 is divisible by 7, which gives us 147=7xCxD or 21=CxD. 21 is 7x3, so we know the four numbers are 5, 7, 7 and 3. But typing in 5773 doesn't work - they have to be in a certain order. The first equation gives the numbers in ascending order (2, 3, 5) so try entering 3, 5, 7 and 7. It works!

I bet the design on the door is some mathematical hint that I'm not recognizing. It looks a little bit like a syntax tree from linguistics, so I bet it's some kind of multiplication factoring tree. Google confirms.