We report the ground state masses of hadrons containing at least one charm and one bottom quark using lattice quantum chromodynamics. These include mesons with spin (J)-parity (P ) quantum numbers (J P ): 0 − , 1 − , 1 + and 0 + and the spin-1/2 and 3/2 baryons. Among these hadrons only the ground state of 0 − is known experimentally and therefore our predictions provide important information for the experimental discovery of all other hadrons with these quark contents. PACS numbers: 12.38.Gc, 14.20.Lq Recently heavy hadron physics has attracted huge scientific interests mainly due to the prospects of studying new physics beyond the Standard Model at the intensity frontier [1][2][3][4][5], and to study various newly discovered subatomic particles to better understand the confining nature of strong interactions [6][7][8][9][10][11][12]. From the perspective of newly found hadrons itself, a large number of discoveries over the past decade ranging from usual mesons [13][14][15][16][17][18][19][20], baryons [21] along with their excited states [22][23][24][25], to new exotic particles like tetraquarks [26-28] and pentaquarks [29], as well as hadrons whose structures are still elusive [6][7][8][30][31][32][33], have proliferated interests in the study of heavy hadrons. Furthermore, it is envisaged that the large data already collected or to be obtained at different laboratories, particularly at LHCb and Belle II, will further unravel many other hadrons. One variety of such theorized but as yet essentially unobserved (except one) subatomic particles are hadrons made of at least a charm and a bottom quarks, the charmed-bottom (bc) hadrons.Investigations of such hadrons are highly appealing, as they provide a unique laboratory to explore the heavy quark dynamics at multiple scales: 1/m b , 1/m c and 1/Λ QCD . Decay constants and form factors of bc mesons are still unknown but are quite important because of their relevance to investigate physics beyond the standard model, particularly in view of the recent measurement of R(J/ψ) [34]. The information on spin splittings and decay constants can shed light on their structures and help us to understand the nature of strong interactions at multiple scales. Moreover, bc baryon decays can aid in studying b → c transition and |V cb | element of the CKM matrix.However, to date the discovery of these hadrons is limited to only two observations: B c (0 − ) with mass 6275(1) MeV [35] and B c (2S)(0 − ) at 6842(6) MeV [36] while the latter has not yet been confirmed [37]. On the other hand, LHC being an efficient factory for producing bc hadrons [38,39], one would envisage for their discovery and study their decays in near future. Precise theoretical predictions related to the energy spectra and decay of these hadrons are thus utmost essential to guide their discovery.In fact various model calculations exist in literatures on bc mesons [40][41][42][43][44][45][46] and baryons [47][48][49][50][51][52][53]. However, those predictions vary widely, e.g. 1S-hyperfine splitting in B c (bc...