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it happened to me too.however i used pencil sharpener which has long blade rather than normal ones and now its ok.but i bet it was a wrong with the pencil type i used .

For me I use the sharpener I use to sharpen my eyeliner pencil.

Just scrub it to a point on a piece of scrap paper.

At an art supply store you can also buy a sharpening paddle which is merely a stack of sandpaper stris attached to a piece of wood.

A pencil sharpener will just keep breaking the soft charcoal.

I've had good success with a scalpel razor and edged it to a pointy tip very slowly.