6
$\begingroup$ 
   1
  1 4
 1 3 3
5 2 2 2

1     salutation
1 4 5 a temptation
1 + 4 is archaic
3 & 4 algebraic
3 + 5 in chess
3 + 4 tasty? yes
2 + 5 removed after kill
2     a journey downhill

Summed for a triangle, what am I?

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  • $\begingroup$ There's a difference between 3 & 4 and 3 + 4? $\endgroup$ – Rand al'Thor Nov 15 at 22:37
  • $\begingroup$ @Randal'Thor Yes; they're different $\endgroup$ – Avi Nov 15 at 23:00
9
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I think I got it:

    S
   I E
  R P I
 N S K I

1 salutation

SIR is a polite salutation

1 4 5 a temptation

A SIREN can tempt you with their songs

1 + 4 is archaic

SIRE is an archaic way of saying "sir"

3 & 4 algebraic

PI and E appear in mathematics quite often, though not so much in algebra

3 + 5 in chess

A PIN is a tactic in chess where you immobilize an opponent's piece by making it so that if your opponent moves it, a more valuable piece is left hanging

3 + 4 tasty? yes

PIE is tasty (yum!)

2 + 5 removed after kill

The SKIN of an animal is the first thing to be removed after a kill

2 a journey downhill

To SKI is to journey downhill

Summed for a triangle, what am I?

You are SIERPINSKI's triangle!

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  • $\begingroup$ rot13(V znqr n zvfgnxr - CV naq R ner npghnyyl genafpraqragny, abg nytroenvp, ahzoref. Bu, jryy :() $\endgroup$ – Avi Nov 15 at 23:17
  • $\begingroup$ Ah, nicely done! $\endgroup$ – Rand al'Thor Nov 16 at 7:59
2
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I don't think this is completely right, but I'll give it a go:

   S
  S M
 E S U
N I K S

1 salutation

???

1 4 5 a temptation

This could be SIN, but it isn't quite fitting.

1 + 4 is archaic

???

3 & 4 algebraic

SUM.

3 + 5 in chess

???

3 + 4 tasty? yes

Similar to YUM?

2 + 5 removed after kill

SKIN.

2 a journey downhill

SKI.

Summed for a triangle, what am I?

Around the edge of the triangle: MUSKINESS.

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  • $\begingroup$ Alternatively, to better solve the first two clues, 4 could be I and 1 could be SUP. But then I don't know about archaic, algebraic, chess, or tasty. $\endgroup$ – Rand al'Thor Nov 15 at 22:59
  • $\begingroup$ ebg13(2 vf pbeerpg, ohg onpxjneqf - cebonoyl gung'yy uryc lbh fbyir gur erfg bs vg) Most everything else is way off, though. $\endgroup$ – Avi Nov 15 at 23:01
  • $\begingroup$ @Avi Is my comment with an alternative approach also way off? $\endgroup$ – Rand al'Thor Nov 15 at 23:03
  • $\begingroup$ Yes, they're both incorrect. $\endgroup$ – Avi Nov 15 at 23:06

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