Is it possible to show that every 1-design $D$ with $\lambda=4,k=4$ on $v$ points (for $v$ that is a multiple of $3$) contain some 1-design $Q$ with $\lambda=1,k=3$ on $v$ points such that every block of $Q$ is some block of $D$ that one of its elements is removed?
a block design question: Does every special 1-design admit a partition which respects enough of the blocks?
j.s.
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