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Abstract This paper is a write-up of the ideas that were presented, developed and discussed at the third International Workshop on QCD Challenges from pp to A–A, which took place in August 2019 in Lund, Sweden (Workshop link: https://indico.lucas.lu.se/event/1214/ ). The goal of the workshop was to focus on some of the open questions in the field and try to come up with concrete suggestions for how to make progress on both the experimental and theoretical sides. The paper gives a brief introduction to each topic and then summarizes the primary results. 

The production of strange hadrons ($$ {\textrm{K}}_{\textrm{S}}^0 $$$K_S^0$, Λ, Ξ^±, and Ω^±), baryon-to-meson ratios (Λ/$$ {\textrm{K}}_{\textrm{S}}^0 $$$K_S^0$, Ξ/$$ {\textrm{K}}_{\textrm{S}}^0 $$$K_S^0$, and Ω/$$ {\textrm{K}}_{\textrm{S}}^0 $$$K_S^0$), and baryon-to-baryon ratios (Ξ/Λ, Ω/Λ, and Ω/Ξ) associated with jets and the underlying event were measured as a function of transverse momentum (p_T) in pp collisions at$$ \sqrt{s} $$$\sqrt{s}$= 13 TeV and p Pb collisions at$$ \sqrt{s_{\textrm{NN}}} $$$\sqrt{s_{\mathrm{NN}}}$= 5.02 TeV with the ALICE detector at the LHC. The inclusive production of the same particle species and the corresponding ratios are also reported. The production of multi-strange hadrons, Ξ^±and Ω^±, and their associated particle ratios in jets and in the underlying event are measured for the first time. In both pp and p–Pb collisions, the baryon-to-meson and baryon-to-baryon yield ratios measured in jets differ from the inclusive particle production for low and intermediate hadronp_T(0.6–6 GeV/c). Ratios measured in the underlying event are in turn similar to those measured for inclusive particle production. In pp collisions, the particle production in jets is compared with Pythia8 predictions with three colour-reconnection implementation modes. None of them fully reproduces the data in the measured hadronp_Tregion. The maximum deviation is observed for Ξ^±and Ω^±which reaches a factor of about six. The event multiplicity dependence is further investigated in p−Pb collisions. In contrast to what is observed in the underlying event, there is no significant event-multiplicity dependence for particle production in jets. The presented measurements provide novel constraints on hadronisation and its Monte Carlo description. In particular, they demonstrate that the fragmentation of jets alone is insufficient to describe the strange and multi-strange particle production in hadronic collisions at LHC energies.