Can you write instructions to survive the tunnel forever?
You wake up in a dark tunnel. There's a cliff to your left and vipers to your right. Your captor demands you write a sequence of LEFT/RIGHT instructions... but they get to choose which instructions you follow.
C=1: Max 11 steps | C=2: Max 1,160 steps | C=3: Unknown (very large)
This puzzle is based on the Erdős Discrepancy Problem, posed by Paul Erdős in the 1930s (with a $500 prize!). The "Prisoner's Walk" framing comes from various mathematical expositions, popularized by James Grime's singingbanana video.
2014: Boris Konev & Alexei Lisitsa proved C=2 has maximum length 1,160 using SAT solvers (generating a 13GB proof!). 2015: Terence Tao proved that NO infinite sequence can have bounded discrepancy, settling the problem completely.