We present detailed chemical abundances for 99 red-giant branch stars in the centre of the Sculptor dwarf spheroidal galaxy, which have been obtained from high-resolution VLT/FLAMES spectroscopy. The abundances of Li, Na, alpha-elements (O, Mg, Si, Ca Ti), iron-peak elements (Sc, Cr, Fe, Co, Ni, Zn), and r- and s-process elements (Ba, La, Nd, Eu) were all derived using stellar atmosphere models and semi-automated analysis techniques. The iron abundances populate the whole metallicity distribution of the galaxy with the exception of the very low metallicity tail, -2.3 <= [Fe/H] <= -0.9. There is a marked decrease in [alpha/Fe] over our sample, from the Galactic halo plateau value at low [Fe/H] and then, after a "knee", a decrease to sub-solar [alpha/Fe] at high [Fe/H]. This is consistent with products of core-collapse supernovae dominating at early times, followed by the onset of supernovae type Ia as early as similar to 12 Gyr ago. The s-process products from low-mass AGB stars also participate in the chemical evolution of Sculptor on a timescale comparable to that of supernovae type Ia. However, the r-process is consistent with having no time delay relative to core-collapse supernovae, at least at the later stages of the chemical evolution in Sculptor. Using the simple and well-behaved chemical evolution of Sculptor, we further derive empirical constraints on the relative importance of massive stars and supernovae type Ia to the nucleosynthesis of individual iron-peak and alpha-elements. The most important contribution of supernovae type Ia is to the iron-peak elements: Fe, Cr, and Mn. There is, however, also a modest but non-negligible contribution to both the heavier alpha-elements: S, Ca and Ti, and some of the iron-peak elements: Sc and Co. We see only a very small or no contribution to O, Mg, Ni, and Zn from supernovae type Ia in Sculptor. The observed chemical abundances in Sculptor show no evidence of a significantly different initial mass function, compared to that of the Milky Way. With the exception of neutron-capture elements at low [Fe/H], the scatter around mean trends in Sculptor for [Fe/H] > -2.3 is extremely low, and compatible with observational errors. Combined with the small scatter in the age-elemental abundances relation, this calls for an efficient mixing of metals in the gas in the centre of Sculptor since similar to 12 Gyr ago.