I very much like your detailed deduction route. Can you please cross-check if your first line - the actual solution - is what you really think it should be for A B C D E being the nominations of the 5 tiles as shown from left to right? (Your solution being DCBEA) I have the suspicion you've made a mistake in the end (but maybe not). I just don't want to pass judgement before I get this confirmation. A B C D E used in the solution are (/should be) the 5 amulets, and NOT your own notation.

@BmyGuest, yes, that's what I think. I've added a tiny bit more explanation to show why.

Very good. (It was the explanation I wanted to tease out of you ;c) ) I'll accept your answer as the correct solution to this puzzle. However, can you please check back to this puzzle after a short time (after I made an edit.) The edit will explain why.

I have accepted your solution, but can you please check the additional bonus question as well?

@BmyGuest, it occurred to me that I muddled up < and > from what I originally thought, and that would give a different explanation. (I also don't think there's any way to tell whether amulet D is positive or negative, which means it's a toss-up between two solutions).

Do you agree that with the additional information above it is no longer ambiguous? Although this puzzle has been 'solved' I would like to tie up loose ends so that other can have a go at it as well.

@BmyGuest, no, I don't, although it does provide pretty good evidence that I muddled up < and >.

Okay, why not? Is there a way we can discuss this without spilling all the beans here? I want to get this puzzled fixed-up proper and you seem to be the person currently best suited to help me.

A small hint (but maybe not enough for proper sorting it). You have not understood the additional hint the way it is meant to. (While true, wouldn't the second line of it be rather trivial, i.e. like 1 <= 1 ? Is it logical, that one would leave such a statement and not rather 1 = 1 ?) Also: There IS already a way of negating the number "C" as you've previously found out....

After having another thought on this, I've modified the additional hint. Satisfactory in your mind?

This is a public chatroom, but it's not so easy to stumble across accidentally as the comment thread.

The latest change just confuses things more. I don't know whether the trapezium in the top line in flipped vertically by mistake or because it's a new symbol, perhaps meaning not-equal-to.

Okay, the thing is that I wand the Hexagon symbol to be the NORM so that the equation reads || a + b || < || a || + || b || which of course you will recognize as triangle inequality. (Hence the shape of the stone as an additional visual clue.)

The extra line was also meant to be || c || = c to indicate which of the c's is the positive. But, you rightfully pointed out that negation would also work. (Albeit there is already the horizontal flip indicating negation.)

So this new line is supposed to take out the possibility of the hexagon denoting a negation. But yes, the flipped over equal sign is a new "not equal". As we already have established what equal is, and what greater/smaller-than are, I thought that the flipping the sign along it's only non-symmetry axis should be clear enough. (I really want these clues to be secondary in importance and not to help you solve the original thing too easily.)

Do you think this is not obvious enough? Basically you have ||-1|| / -1 != || 1 || / 1 whereas for negation you would get -(-1) / (-1) == -(1)/(1).

It introduces 5 new symbols in two lines. To get the right interpretation requires making quite a few guesses with little to guide you.

And using norms is quite a jump in mathematical sophistication: from primary school level to something which doesn't seem to be discussed in European mathematics until the 19th century.

Well, as for the sophistication I think once we reach different number-bases math-level has reached a certain level. Also the other deductions weren't easy. So the questions is not, is it "hard" to get it right, but are those "guesses" allowing for a different interpretation? And of course: Do you have a other good suggestion for solving this ambiguity without being to obvious?

Sure. You can disambiguate the sign of amulet D with a single inequality containing +D and -D.

Right. (Only if the < and > are disambiguated first, though, but that's taken care of in the triangle-inequality.) Would you approve of such a modification ?

The triangle inequality takes care of it really by showing a <= symbol, not by being the triangle inequality.

Alternative, arguably simpler, interpretations which fit the identities given are that the coffin box is the successor function or that it's the round-up-to-even function.

So a single -D <= D would take care of both issues.

Not sure I follow with your first statement. It's the tilting-direction that is of importance for problem 1 ( < or > ? ). I thought having some recognizable inequality (to mathematicians at least) should solve that. The C or -C problem was a complete overlook on my part, and I think adding a "-C < C" to the original stone would be best.

(BTW, the reasoning for "lesser than" is that the symbol represents scales being equal or tilting to the heavier side)

If the single trapezium cannot be <= but must be either < or >, it must be > unless one digit value has multiple symbols or the solution is even more ambiguous.

I finished the original solution at about 1 a.m., which is probably why I reasoned that when I got e symbol 10(decimal) it must be <= rather than <. If I'd been more awake I'd probably have spotted that I'd flipped the symbol from my initial assumption, which was exactly that it was tilting to the heavier side.

Ah! yes, now I see. Sounds like the smallest solution then. If you agree, I will take out the "amendmend" alltogehter and add the one line ( -D <= D ) to the original tomb stone. You could modify your answer accordingly and all is fine for hte future... a

Yes, you might have done so - and I would never have discovered the flaw. Good you're puzzling at 1 a.m. ! :c)

Ok. It might be an hour before I update my answer.

Sure, same here. (I've actual work to do as well ;c) ) Thanks a lot though.

Ok, I've updated my answer and deleted my comments to it, which are now obsolete. I suggest you delete those of your comments which are also obsolete.

(And as a side-comment on something you said earlier, I disagree that "once we reach different number-bases math-level has reached a certain level". The Babylonians used base 60 about 3000 years ago. There are remnants of base 12 in English and other Germanic languages. The idea that base 10 is natural because we have ten fingers seems ahistorical: using a base with good divisibility properties seems to have been more natural to many cultures).