3 problems

Crew–Narayanan–Spirkl conjecture. There is a partition $[n]=P\cup Q$ into two nonempty sets and a partition $S^1=X\cup X^c$ into two intervals such that

Identity-assignment partition conjecture. There exists a positive integer $r$ such that the plane can be partitioned, using $r$ lines, into $2k$ not necessarily connected regions…

Grünbaum's conjecture. For every $t\in[0,1/4]$, there exists a pair of orthogonal lines that partitions $P$ into four pieces whose areas, in clockwise order, are…