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We prove upper and lower bounds on the effective content and logical strengthfor a variety of natural restrictions of Hindman's Finite Sums Theorem. Forexample, we show that Hindman's Theorem for sums of length at most 2 and 4colors implies $\mathsf{ACA}_0$. An emerging {\em leitmotiv} is that the knownlower bounds for Hindman's Theorem and for its restriction to sums of at most 2elements are already valid for a number of restricted versions which havesimple proofs and better computability- and proof-theoretic upper bounds thanthe known upper bound for the full version of the theorem. We highlight therole of a sparsity-like condition on the solution set, which we call apartness.

New bounds on the strength of some restrictions of Hindman's Theorem