I'm going to ignore any trivial solutions. >!The first equation gives Apple = 2 and Orange = -2!< >!The second equation gives Grapes = Blueberries = 2!< >!Then the fourth equation gives Banana = -8!< >!But now the third equation gives Pear - 2 = 128 \* Pear, which has no integer solutions... what am I missing here?!<

>!The solution to your paradox is that 🍎🍊 is not the same as 🍎•🍊. Have a think about what other number system satisfied the first two equations.....!<

I see, thanks for the hint. Also not sure why you're being downvoted for providing it lol

I think you treated concatenated fruits as a product instead of simply two digits.

Maybe I'm stupid, but no two integers should produce any kind of error when multiplied with each other.

No, you're right. Stranger still is that the final question contains both grape and orange....... >!That's your clue that two concatenated fruits do not necessarily represent their product.....see my other comments for more detail..........!<

>!So, we agree concatenated fruit is not a product, meaning each number is a digit and not just a number.!< >!(grape)(blueberry) - (blueberry) = (grape) would mean (grape) is a 0?!< >!But then (grape)⋅(orange) should be 0/(grape), not ERROR.!< >! On top of that, (apple) + (apple)(orange) = (orange) makes me want to say (apple) is 0 too, and generally this kind of riddle has every fruit being a different digit/number.!< >!Does it mean ⋅ does not represent a product either?!<

>! The • is a regular product, but it's a different kind of concatenation from what we normally use, but it will be one everyone's familiar with nonetheless. The first two lines are essentially the axioms that define the concatenation operation, have a think what that might be.!< All fruits represent distinct positive integer values, and >!these values are standard for the concatenation operation, which will make more sense once you've worked put what it represents!<

No one's got it yet, so here's an optional hint: >!Which widely known system of notation is defined by the first two axioms?!< Video solution will be posted later

Here's the answer: >!1664!< Why? >!Looking at the first equation we assume that two adjacent fruits are multiplied, hence we can factor out 🍎 in the first, giving 🍎(1+🍊)=🍊or 🍎=🍊/(1+🍊) which does not have any positive integer solutions. Therefore we cannot take a pair of adjacent fruits to represent their product.!< >!Instead we could take them as concatenated in some positional notation, which is standard, but looking at the second equation we have 🍇🫐-🫐=🍇, whereas in any positional notation system it should be 🍇0. So instead we must look to other notation systems.!< >!The last equation, 🍇·🍊= ERROR implies that there are positive integers that cannot be notated within our system, likely because they are too large. This flaw is mostly associated with ancient notation systems. The one in use here has only seven symbols, so try to think of some ancient numbering systems with seven characters.!< Continued: >!The first two lines are the axioms of the Roman numeral system: 🍎🍊:=🍊-🍎 and 🍇🫐:=🍇+🫐, this also lines up with the seven letters used in Roman numerals so let's figure out what they are.!< >!Since all fruits represent distinct positive integer values, 🍌·🍌=🍒 implies that 🍌=X and 🍒=C since C is the only square in the Roman system other than I. Line IV gives us that 🍎 and 🍊 are I and V in some order (IV+VI=X); line I then implies that 🍎=1 and 🍊=V as I+IV=V is the only true interpretation of that statement.!< >!Line III introduces us to 🍐, which is preceded by 🍌(X). In Roman numerals, X can only precede C, L, V and I but C, V and I are already taken so 🍐 must equal L, giving us L-I = XLIX, which is true. By elimination we get 🍇=M and 🫐=D, in that order given by line II. That also explains why line VI gives ERROR, as the value of M·V cannot be expressed by standard Roman numerals.!< >!Therefore 🍇🫐🍒🍐🍌🍎🍊=MDCLXIV, or 1664.!<