an honest question to you

I have one particular student that is really making me question every ethical belief I have.
I so badly want to kick him with all the strength that my 5'1" self can muster.

Here's the situation:
Class starts.
The warm-up is always projected when the students come in. Every day.
Everyone is working on the warm-up, except for him.
I ask him, "Why aren't you doing the warm-up?"
Him: "What? What warm-up?"
I point at the front of the classroom while I keep my eyes locked on him.
Then he acts genuinely surprised that there is a warm-up on the board!
Him: "Oh! I didn't know!"

Then!
A few minutes later, he's still doing nothing.
Me: "What are you supposed to be doing?"
Him: "I don't have a pencil."
Me: "You know where to find extra pencils. On the back counter in the blue cup."
Him: "Oh, okay."

Then--next activity.
Me: "Why aren't you taking notes?"
Him: "I don't have a pencil."
Me: "What happened to the one you used for the warm-up?"
Him: "I lost it."
what? how do you lose a pencil in five minutes?
But it's not worth me stopping the whole class every day to have him search for a pencil.
So I tell him to go grab another one from the back.

This same conversation happens every day, five times a day.
I always ask him, "How did you write in your last two classes?"
Him: "I didn't have to write anything."
Me: "Well, I know that's not true.  I'm good friends with your English teacher--we talked about YOU and she said you always borrow a pencil in her class.  What happened to the one you borrowed from her today?"
Him: "I lost it."

Someone strangle me!
(or him..)
What the heck is he doing with all of these pencils?
Is he saving them up to build a house or something?
Because if he his, I'm sure I've financed a whole first floor worth of pencils.

I should also mention that I have devoted so much time and energy with this student.
I'm invested in a lot of students--but I really feel invested in him.
At the end of last term, he had an F--a 37%.
I told him that if he took a test he was missing and actually tried on it, then I would pass him.
I sat down with him for 2.5 hours.
I studied with him.
I gave him all of the answers!
The next day, he came to take the test.
And I caught him looking at his phone for all of the answers.
I almost cried.
C'mon, we worked SO hard together!
We talked it out, and he understood that I couldn't pass him.

My question to you: how do I solve my daily dilemma with him!?
important note: this student has no special accommodations.
he is a perfectly functioning child, who is just perfectly lazy.

Solution A: I give him one pencil a day.  If he loses the pencil, then too bad.
Problem to Solution A: is it more important for him to take notes and participate than to sit doing nothing so that I can prove a point?

Solution B: I give him a pencil every time he needs one.
Problem with Solution B: Am I just holding his hand? Am I teaching him anything about responsibility? Everyone else comes prepared--why can't he? Plus, he is emptying my little blue cup of all the pencils, so the kid who comes prepared 99% of the time won't have a pencil on the off-chance he forgets his today.
and remember: on average, he takes THREE pencils a day.
that's a FACT!

Solution C: I never give him a pencil.
Problem with Solution C: Again, what's more important? Him doing the work? Or trying to teach him responsibility?

I feel like I've tried all of these solutions, only to be frustrated all over again.
Someone give me another solution, or help me realize why one of the above solutions is better than the others.
ah geesh, these teenagers.
I love them to death.
but that death may come a lot earlier than anticipated...
because of them.
I'm aging by the minute!

sooo...solve my problem?
thanks.