We will talk about the smooth (resp. topological) ℂℙ2–slicing number of knots, i.e., the smallest m≥0 such that a knot K in S3 bounds a smooth (resp. locally flat), properly embedded, null-homologous disk in a punctured connected sum of m copies of ℂℙ2. We will give a lower bound on the smooth ℂℙ2–slicing number of a knot in terms of its double branched cover, and we find knots with arbitrarily large but finite smooth ℂℙ2–slicing numbers. We will also give the first examples of knots where the smooth and topological ℂℙ2–slicing numbers are finite, distinct and simultaneously nonzero. This is a joint work with A. Kjuchukova, A. N. Miller, and A. Ray.