11
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My first is really easy - trust me, it's not hard.
Fail here and you will kick yourself.
In rhymes it's found with Simon seeking lard;
In maths it doesn't meet itself.

My second is found right here on this site:
Read on with prudence
and drop the penny
Some say I'm one, I say I'm many.

My third makes clear you've got it right:
A pleasant sight to many students.
Or it might be a parasite,
Head in deep with every bite.

Put them together, form a whole,
And a single longer word you'll find.
When you've got it, take a stroll
Over here where clues are combined.

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16
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The first is surely

SIMPLE

My first is really easy - trust me, it's not hard.
Fail here and you will kick yourself.

Simple = not hard. If you fail to solve something simple you will be annoyed.

In rhymes it's found with Simon seeking lard;

Simple Simon met a pieman...

In maths it doesn't meet itself.

Simple closed curve.

The second is probably

LIST

My second is found right here on this site:

Lots of lists. List of puzzles, Hot Network Questions, list of users, etc., etc., etc.

Read on with prudence
and drop the penny

This seems like it ought to point to (P)ERUSE or (P)ORE or something, and so far as I know nothing of the kind works ... But see below.

Some say I'm one, I say I'm many.

A list is one thing made up of many things.

So, what about those not-really-fitting lines 2 and 3? Well, the link provided by an anonymous user in comments shows that essentially the same clues have been given for the same answer in another puzzle a couple of years ago, and then those two lines were just filler. I have to say I find this a bit unsatisfactory -- it wasn't fair then, and it isn't fair now -- but never mind :-).

I agree with Mithrandir: the third is clearly

TICK.

Putting them together yields

SIMPLISTIC.

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  • 1
    $\begingroup$ Does this help with the second part: puzzling.stackexchange.com/questions/4790/the-egocentric-one/… $\endgroup$ – user1566694 Nov 21 '16 at 18:28
  • $\begingroup$ Well, it helps in that it suggests that the two lines that were puzzling me were just filler, and if I happened to have memorized every puzzle posted here for the last two years I'd have recognized the fact :-). Fair enough, I guess. $\endgroup$ – Gareth McCaughan Nov 21 '16 at 18:54
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    $\begingroup$ It would've been enough to just put "Read on with prudence and drop the penny" into the search box :-) Good job on this, and hat tip to @user1566694 for finding the intended meaning of the 2nd verse. $\endgroup$ – Rand al'Thor Nov 21 '16 at 20:38
  • $\begingroup$ Well, yes, if I'd guessed that that bit of the clue might be taken verbatim from an old puzzle. That's not a guess I usually make (though I might make it more often in future). $\endgroup$ – Gareth McCaughan Nov 22 '16 at 0:13
  • $\begingroup$ Can I link your mention of my answer to it? $\endgroup$ – Mithrandir Nov 22 '16 at 13:09
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Partial Answer

Second:

P

My second is found right here on this site:

Puzzling

Read on with prudence

starts with P

and drop the penny

Also

Some say I'm one, I say I'm many.

Could this be a reference to p orbital?

The third:

Is probably a tick.

My third makes clear you've got it right:

Like here - a green check means correct

A pleasant sight to many students.

I bet it is

Or it might be a parasite,
Head in deep with every bite.

The bug called a tick

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