What Does It Mean?: Hints

• As you may have already found with the answer checker, the answer isn't simply "hexoctahedron", as it might seem from the flavortext.
• This hint slightly clues an aha moment. The text of the puzzle (apart from the flavortext) is a series of lines, all with a certain property, which will be called acceptability thoughout the rest of these hints.
• This hint slightly clues an aha moment. Any acceptable line, or set of lines, could be added to the puzzle, and this would almost certainly, if anything, make it easier to solve.
• This hint slightly clues an aha moment. The main important thing to do in solving this puzzle is figure out what the property all the given lines has is, and how to determine if a line has it.
• This hint slightly clues an aha moment. The separation between sets of lines is not necessary to solve the puzzle, and serves to break the lines into smaller subsets within each of which all the lines are similar in some way.
• This hint slightly clues an aha moment. Reading the lines in order is a good place to start.
• This hint slightly clues an aha moment. Look at the first six lines. What do they all have in common?
• This hint slightly clues an aha moment. Do you think edw would be acceptable?
• This hint slightly clues an aha moment. edw would not be acceptable.
• This hint slightly clues an aha moment. Looking at the next three sets of six lines, we have etdww at the start of the second set (counting the first six lines we've already looked at as the first set) and ewtdw at the start of the fourth set.
• This hint slightly clues an aha moment. Recall our guess for acceptability of e followed by two single letters. What does this suggest about tdw and w, since etdww and ewtdw are both acceptable?
• This hint slightly clues an aha moment. Is there anything similar to the above that can be said about, for example, twv and b? By the way, the next hint gives additional information about e, so if you don't want that additional information yet don't read any more hints.
• This hint clues an aha moment and gives away a small part of that aha moment. e can be thought of equivalence, in some sense, of the two things following it.
• This hint clues an aha moment. The above tells us that, using ~ for equivalence, tdw ~ w, tww ~ c, twc ~ v, twv ~ b, tbw ~ u, and apparently tuw ~ xcv.
• This hint clues an aha moment. Using the third set of six lines, we see that all these equivalences are also true if the two characters following t are swapped (so, for example, twd ~ w).
• This hint clues an aha moment. The fifth set of lines, this one with only three lines, tells us that tdc ~ c, tcc ~ b, and tbc ~ xcv.
• This hint clues an aha moment. You can keep proceeding in this way to get some more equivalences involving t.
• This hint clues an aha moment. Is there any meaning t could have, and that d, w, c, v, b, and u could have, that would explain these equivalences?
• This hint strongly clues an aha moment. Is there anything looking sort of like t (lowercase t) that might be relevant?
• This hint gives away most of an aha moment. The rest is given away in following hints. t is + (except it takes its two operands after it, rather than one before and one after). The next hint gives away what d, w, c, v, b, and u are.
• This hint gives away some of the rest of the above aha moment. d, w, c, v, b, and u are 0, 1, 2, 3, 4, and 5, in that order. The next hint gives away exactly what e is, if it isn't already clear.
• This hint gives away some of the rest of the above aha moment. e is =. From now on hints will be more gentle guides to figuring out what is what, rather than saying it directly. There are some exceptions which will be clearly stated beforehand so you don't accidentally spoil yourself.
• s and x should now not be that hard to figure out.
• For the two first sets of lines all beginning with f, look at what's not included.
• For example, there's no line that's fedd, and indeed fedd is unacceptable.
• Now that you know what f is, l and g shouldn't be that hard.
• There are some lines that use e twice, and some that use f in a non-initial position. Knowing the conventions for false and true in programming might help here; these conventions are stated in the next two hints.
• False is generally zero, true is generally one. (In some programming languages this is literally true, in some it's only mostly true.)
• If a number is considered true or false, any number other than zero is generally considered true; zero is generally considered false.
• Determining what z, q, r, j, and k are is now not that hard.
• h, o, a, and n are a little confusing. The next few hints help somewhat with those.
• a can only occur directly before h.
• h arguably has a different meaning when directly preceded by a.
• a can only occur directly after t, x, j, and k.
• t, x, j, and k have somewhat different meanings when directly followed by a.
• o must be following (not necessarily directly following) h.
• n must be following (not necessarily directly following) two occurences of h (not necessarily consecutive). The next hints explain exactly what h, o, a, and n do (in that order). There are two hints devoted to a.
• This hint gives away some of the rest of the above (now far above) aha moment. h is usually (that is, not directly after a) "having the property that".
• This hint gives away some of the rest of the above aha moment. o is a reference to the number potentially having the property. So, for example, heovv means that 3 (v, the second one) has the property described by heov, that is, the property (h) of equality (e) between it (o) and 3 (v, the first one). In other words, heovv means that 3 has the property of being equal to 3.
• This hint gives away some of the rest of the above aha moment. a is "the list of all positive integers" (not including 0), so ah is "the list of all positive integers having the property that". The next hint is about the meaning of t, x, j, and k before a.
• This hint gives away some of the rest of the above aha moment. t, x, j, and k before a combine all the numbers in the list. So, for example, t preceding a list is that list's sum.
• This hint gives away some of the rest of the above aha moment. n is used when one property definition (via h) is nested in another to refer to the number in the inner property definition. In this case, o refers to the number in the outer property definition. So, for example, hetahlnovv means that 3 (second v) has the property (first h) that the sum of all the positive integers (tah) with the property that they (n) are less than (l) it (o) is (e) 3 (first v). Stated without the parenthesized letters, this says that 3 has the property that the sum of all the positive integers less than it is 3, which is true. Compare to etahlovv, which says more simply that the sum of all the positive integers less than 3 is 3.
• Now that we know what all the letters mean, what can we do?
• This hint clues an aha moment (a new one; the above one is done). That "hexoctahedron" in the flavortext isn't completely irrelevant.
• This hint clues an aha moment. The answer is hexoctahedron, in a sense.
• This hint gives away an aha moment. The above method of interpreting letters lets hexoctahedron have a meaning that's a property of numbers.
• The property of numbers that's the meaning of hexoctahedron is well-known.
• In fact, it has a name.
• If you're having trouble figuring out what the property is, trying some numbers might help.
• This hint suggests a method of doing research, and since it's the last hint, asking whether it can be skipped is meaningless. After finding some numbers with the property (and some without, so you can eliminate overly-broad guesses for the property), if you still don't know the property's name, searching those numbers might help. If you have only one or two such numbers, adding other relevant keywords or looking on some reference page for properties of numbers might be useful.