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An analysis of $B^{\pm}\to DK^{\pm}$ and $B^{\pm}\to D\pi^{\pm}$ decays ispresented where the $D$ meson is reconstructed in the four-body final state$K^{\pm}\pi^{\mp} \pi^+ \pi^-$. Using LHCb data corresponding to an integratedluminosity of $1.0{\rm \,fb}^{-1}$, first observations are made of thesuppressed ADS modes $B^{\pm}\to [\pi^{\pm} K^{\mp}\pi^+\pi^-]_D K^{\pm}$ and$B^{\pm}\to [\pi^{\pm} K^{\mp} \pi^+\pi^- ]_D\pi^{\pm}$ with a significance of$5.1\sigma$ and greater than $10\sigma$, respectively. Measurements of CPasymmetries and CP-conserving ratios of partial widths from this family ofdecays are also performed. The magnitude of the ratio between the suppressedand favoured $B^{\pm}\to DK^{\pm}$ amplitudes is determined to be $r^K_B =0.097 \pm{0.011}$.

Observation of the suppressed ADS modes $B^\pm \to [\pi^\pm K^\mp \pi^+\pi^-]_D K^\pm$ and $B^\pm \to [\pi^\pm K^\mp \pi^+\pi^-]_D \pi^\pm$