An analysis of B±→DK±B±→DK± and B±→Dπ±B±→Dπ± decays is presented where the D meson is reconstructed in the four-body final state K±π∓π+π−K±π∓π+π−. Using LHCb data corresponding to an integrated luminosity of 1.0fb−1, first observations are made of the suppressed ADS modes B±→[π±K∓π+π−]DK±B±→[π±K∓π+π−]DK± and B±→[π±K∓π+π−]Dπ±B±→[π±K∓π+π−]Dπ± with a significance of 5.1σ and greater than 10σ, respectively. Measurements of CP asymmetries and CP-conserving ratios of partial widths from this family of decays are also performed. The magnitude of the ratio between the suppressed and favoured B±→DK±B±→DK± amplitudes is determined to be rBK=0.097±0.011.