Why does the final return reveal the loop?
The observer can inspect only one candle, but a toggled candle persists as local state. Choose the strongest invariant.
Choose after discovering the loop.
Count a loop you can never see.
One candle at a time. No chalk, no map, no known length. Use switch state as local memory and make every visit count.
Hidden loop awaiting your first prediction.
Predict guess 10
Choose what guess 10 means before probing.
Guess10
Visits0
Found N?
LOCAL VISIBILITYBINARY SWITCH MEMORYUNKNOWN NEXPONENTIAL BOUNDFINAL WRAP COUNTLOCAL VISIBILITYBINARY SWITCH MEMORYUNKNOWN NEXPONENTIAL BOUNDFINAL WRAP COUNT
A changed switch remembers what you cannot mark.
Transfer to any finite loop
Why does doubling help if it does not itself reveal exact N?
Apply the strategy beyond the 12-candle example.
Loop field record
Discover the loop, verify the invariant, and solve the transfer challenge.
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reasoning checks complete