This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. The material presented here is based on work supported in part by NASA under contract no. NNX15AI75G. TRAPPIST-South is a project funded by the Belgian Fonds (National) de la Recherche Scientifique (F.R.S.-FNRS) under grant FRFC 2.5.594.09.F, with the participation of the Swiss National Science Foundation (FNS/SNSF). TRAPPIST-North is a project funded by the University of Liège, and performed in collaboration with Cadi Ayyad University of Marrakesh. The research leading to these results has received funding from the European Research Council (ERC) under the FP/2007-2013 ERC grant agreement no. 336480, and under the H2020 ERC grant agreement no. 679030; and from an Actions de Recherche Concertée (ARC) grant, financed by the Wallonia–Brussels Federation. The VLT data used in this work were taken under program 296.C-5010(A). UKIRT is supported by NASA and operated under an agreement among the University of Hawaii, the University of Arizona, and Lockheed Martin Advanced Technology Center; operations are enabled through the cooperation of the East Asian Observatory. The Liverpool Telescope is operated on the island of La Palma by Liverpool John Moores University (JMU) in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias, with financial support from the UK Science and Technology Facilities Council. This paper uses observations made at the South African Astronomical Observatory (SAAO). M.G., E.J. and V.V.G. are F.R.S.-FNRS research associates. B.-O.D. acknowledges support from the Swiss National Science Foundation in the form of a SNSF Professorship (PP00P2_163967). E.A. acknowledges support from National Science Foundation (NSF) grant AST-1615315, and NASA grants NNX13AF62G and NNH05ZDA001C. E.B. acknowledges that this work is part of the F.R.S.-FNRS ExtraOrDynHa research project and acknowledges funding by the European Research Council through ERC grant SPIRE 647383. S.N.R. thanks the Agence Nationale pour la Recherche (ANR) for support via grant ANR-13-BS05-0003-002 (project MOJO). D.L.H. acknowledges financial support from the UK Science and Technology Facilities Council. The authors thank C. Owen, C. Wolf and the rest of the SkyMapper team for their attempts to monitor the star from Australia; from UKIRT, the director R. Green and the staff scientists W. Varricatt and T. Kerr; the ESO staff at Paranal for their support with the HAWK-I observations; JMU and their flexibility as regards the Liverpool Telescope schedule, which allowed us to search actively for the planets, and to extend our time allocation in the face of amazing results; for the William Herschel Telescope, C. Fariña, F. Riddick, F. Jímenez and O. Vaduvescu for their help and kindness during observations; and for SAAO, the telescopes operations manager R. Sefako for his support.