Not an affix-riddle at all

Slice my neck, that's quite epic.
Slice my thigh, that's quite demonic.
Slice my waist, you shall have a kill.
Slice all three, that's an overkill.

What am I?

Subtle hint:

I have only one thigh. That's why "thigh" above is singular.

Moderate hint:

Slicing my neck or my thigh doesn't kill me entirely.

Decisive hint:

The branch of math in concern is algebra.

Very decisive hint:

Slice nothing, my waist is invertible.

• Is it actually a mathematics riddle? Aug 9 '21 at 11:47
• @ExtraFishness Yes. Aug 9 '21 at 18:25
• Fishing for a hint... Is the title merely to stop us from falling into a trap for the format, or is it actually a bigger tongue-in-cheek hint? And, is there any amount of real world trivia/knowledge involved? Aug 16 '21 at 23:15
• @Feryll The title merely indicates this riddle is not an affix-riddle. Also, "knowledge" tag is added. Aug 16 '21 at 23:26
• I see, thank you. And just to be sure we're on the same page regarding the mathematics tag: "A puzzle related to mathematical facts and objects, whose solution needs mathematical arguments." Does the latter half of this description apply, or only the former? I.e. is the solution just the alignment of known factoids and their relation to the text, or does semi-original math need to be performed? Aug 16 '21 at 23:37

Our object is

a very short exact sequence $$0\rightarrow A\rightarrow B\rightarrow 0$$. "Exact sequence" means that the image of each function is the kernel of the next one. Here $$A,B$$ are, let's say, groups and $$0$$ is the trivial one-element group. (You can do similar things with other structures besides groups.) The left-hand side is the head end, which seems the wrong way around because the right-hand side is where the arrow-heads are, but never mind.

Slice my neck, that's quite epic.

Remove the leftmost arrow, leaving $$A\rightarrow B\rightarrow 0$$. This says that the image of the $$A\rightarrow B$$ map is all of B; that is, that that map is epic ("onto").

Slice my thigh, that's quite demonic.

Remove the rightmost arrow, leaving $$0\rightarrow A\rightarrow B$$. This says that the kernel of the $$A\rightarrow B$$ map is trivial; that is, that the map is monic ("one-to-one"). The "de" at the start of "monic" is just there to make the technical term "monic" into an ordinary word.

Slice my waist, you shall have a kill.

Remove the $$A\rightarrow B$$ arrow itself and the object of interest (namely, the map represented by that arrow) is no longer there; it's been killed.

Slice all three, that's an overkill.

Now there's nothing left at all, which seems a reasonable definition of overkill.

Hints:

1. Only one thigh: yes, there's just a linear sequence of arrows. 2. Removing neck or thigh still leaves the $$A\rightarrow B$$ arrow there and tells us something about it. 3. Yes, this is algebra. 4. If we don't do any slicing we have an exact sequence $$0\rightarrow A\rightarrow B\rightarrow 0$$ which implies that the $$A\rightarrow B$$ arrow is an isomorphism ("invertible").

• Extremely close! Aug 23 '21 at 20:56
• If "an exact sequence" were the answer, it would probably mean "slice my waist/get a kill" to mean "if B = 0, then necessarily A = 0 and C = 0." Note that this "killing" isn't true if you slice the "thigh" (force C = 0 to be epic) or the "neck" (force A = 0 to be monic). Aug 23 '21 at 22:10
• However, I'm still not sure why it would be "neck" and "thigh" rather than anatomy more common in riddles, like "head" and "leg," unless there were some specific reason. As well, category theory isn't really algebra, even if it finds use there. Nor would I understand the "overkill" line, unless we just read "kill = overkill." Aug 23 '21 at 22:17
• Here are some links that may be relevant. en.wikipedia.org/wiki/Category_theory en.wikipedia.org/wiki/Arrow_(symbol) ||| ↠ epimorphism (or epic) (surjective function) en.wikipedia.org/wiki/Epimorphism en.wikipedia.org/wiki/Surjective_function ||| ↣ monomorphism (or monic) (injective function) en.wikipedia.org/wiki/Monomorphism en.wikipedia.org/wiki/Injective_function ||| "Slice my waist, you shall have a kill." This could be referring to endomorphism (kill = end) en.wikipedia.org/wiki/Endomorphism Aug 23 '21 at 22:29
• Sorry forgot there is no formatting in comments. But anyway, the thing about the "endomorphism" idea is that it doesn't seem like there is a symbol used to indicate endomorphism, so not sure how to connect it to the "slice my waist" clue. -- On the other hand, there is the idea of "dashed arrows" used to claim the existence of a morphism, as this page mentions: en.wikipedia.org/wiki/Commutative_diagram but not sure how to connect that to the "you shall have a kill" clue Aug 23 '21 at 22:30

Okay this may be stretching it a bit but I'm gonna post it anyways cuz its been 2 weeks with no answer...

The number 8

This answer was heavily influenced by

Slice my neck, that's quite epic

Imagine the written out 8. If you cut of the top portion, it looks like this:
This symbol is 4 in Hindi, which is what you get if you slice 8 in half. Thats pretty epic

Slice my thigh, that's quite demonic

If you go from the thigh up, it is about 3/4th of the body. 3/4 * 8 = 6. 6 is the number of the beast, which is demonic.

Slice my waist, thats a kill

Cutting the middle of the 8 yields a 0. There's nothing left, so its dead.

Slice all three, thats overkill

This could be a play on words... you could draw a line down the center dividing the figure into a 3 and a 3rotated 180deg as shown here:

removing all the threes would leave blank space. Nothing remains again, but this physically removes everything rather than just leaving a representtion of nothing (0).

Yeah so this is probably wrong... but I mean no one else is answering so lets give it a shot!

• That's quite creative, but not what I intended. 😅 Nonetheless, +1 from me! Aug 20 '21 at 4:06
• @DannyuNDos I look forward to seeing the answer. Perhaps another hint is in order. Aug 20 '21 at 16:34

a rhombus.

It fits the first 2 lines somewhat nicely.

Slicing the upper half gives you a downward-looking pentagon, which is associated with the Superman symbol hence epic. Slicing the lower half gives an upward-looking pentagon which is associated with a pentagram hence demonic.

The other 2 lines don't fit that well but maybe

kill means triangulation. When you slice the rhombus in the middle you get 2 triangles. If you slice the middle horizontally and both upper and lower halves vertically you get 4 triangles (an "overkill").

First post here, sorry if I did something wrong.

Continuing on from my comment, I have an interpretation of what I feel could be an answer, but given there are 3 of them I'm uncertain I'm even on the right track.

In my comment I postulated that the "slice" indicated division.

Working backwards from the assumption I multiplied 666 by 1-9 to determine 4-digit numbers that would satisfy the "slice my thigh" (between 3rd and 4th digits) and came up with four numbers: 1332, 2664, 3996, and 5328. Of those four numbers, the first 3 all have an interesting property to them.

When you "slice" their neck (1/3322, 2/6644, and 3/9966) they all result in 0.000301204... which is interesting and could be considered "epic".

When you "slice" their waist (13/322, 26/644, and 39/966) they all result in 0.04037 which is also surprising and may confirm (or make the "kill") to their significance. And when you "slice" their thigh (1332/2, 2664/4, and 3996/6) they all equal 666. Slicing all three (1/3/32/2, etc.) is overkill, and no longer keeps to the pattern.

• I don't understand how you are doing the division. 133/2 is 66.5, not 666...
– wimi
Aug 24 '21 at 19:15
• Drat... 666*2 = 1332. I messed up. In this case it would have to be 1332/2, so the whole thing is busted. Thanks for the catch. Aug 24 '21 at 22:42
• There, adding the additional number at the end makes them all work now. e.g. 13/322 = 26/644 and 1/3322 = 3/9966 etc. Aug 25 '21 at 0:51