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The Ramsey number    r  (   K  s   ,   Q  n   )    is the smallest positive integer   N   such that every red–blue colouring of the edges of the complete graph    K  N    on   N   vertices contains either a red   n  ‐dimensional hypercube, or a blue clique on   s   vertices. Answering a question of Burr and Erdős from 1983, and improving on recent results of Conlon, Fox, Lee and Sudakov, and of the current authors, we show that    r   (   K  s   ,   Q  n   )   =   (  s  −  1  )    (   2  n   −  1  )   +  1    for every    s  ∈  N    and every sufficiently large    n  ∈  N   .

The Ramsey number of the clique and the hypercube