Stuck on weights/metals puzzle in Alchemists level

[Scribblor]

Could someone explain how to solve this puzzle please?

I have filled the machine with silver and gold, and I found the formulae inside laboratory 3, so I think I have all the necessary information.

I've used the adding machine to transcribe the formulae into numbers, but then when I get to the transform machine, I can't figure out the relationship between the numbers or the formulae glyphs and the available weights.

Ideally I'm not looking for the solution, but an explanation of how the puzzle works so I can solve it myself.

I'm probably missing something obvious, and I've looked up a couple of YouTube playthroughs, but even looking at the solution there, I don't understand how the people playing through are solving it. They seem to be choosing at random (though they clearly aren't).

Thanks :)

[Nixmachine]

1. The number system that the scientists use is the same as ours - a decimal system. They use numbers from 0 to 9999 in one "glyph". For example, the password you used to enter Lab 3 is a 4-digit number. Upper left - Upper right - Down left - Down right is the order of the numbers.

2. The formulae has 3 elements and each one has a corresponding number. The transformation machine has an abundant supply of elements. The formula is probably about how much each element is needed to make the key

2. Look at the weights on the transformation machine. There are numbers written on the weights. The smallest one has 1 written on it, while the largest one has 500 written on it. How about adding the numbers on the weights to match the number written beneath each element glyph?

[Scribblor]

Thank you SO MUCH! I was indeed missing something obvious - I totally misunderstood what you explain in point 1.

I didn't realize the four 'quadrants' of the number were ones, tens, hundreds and thousands. Now it makes total sense!

[BoonMike]

What helped me with this puzzle was even when I was confused about the order of the numbers (i.e. which part of the quadrant is tens, hundreds, etc) certain combinations are impossible with the limited weights that you're given, so if all else fails you can still use the weights to work out which order the numbers *must* be in.

[The Cakemeister]

It's worth noting that there is a calculator on the shelf of lab 2, (presumably where you learned 6-9, and 0) You can input two numbers in our adding system and see them added together and displayed as a singular glyph.

[Myriad Destiny]

Originally posted by Scribblor:

Thank you SO MUCH! I was indeed missing something obvious - I totally misunderstood what you explain in point 1.

I didn't realize the four 'quadrants' of the number were ones, tens, hundreds and thousands. Now it makes total sense!

fun fact, there's a real medieval number system that works very similarly, called Cistercian Notation. Numberphile made a video on it ages ago. I made the connection almost immediately, just didn't know the exact order of the digits.

[General WVPM]

Originally posted by The Cakemeister:

It's worth noting that there is a calculator on the shelf of lab 2, (presumably where you learned 6-9, and 0) You can input two numbers in our adding system and see them added together and displayed as a singular glyph.

So it's just a calculator. I was stuck here entering the number found on the note.

[TowerWizard]

First time I did this puzzle, I failed because the order or elements in the machine were silver gold copper, and not gold silver copper...