Case 40 · cipher / binary · Medium · About 8–12 minutes
A harbor signal keeper has copied six rows from a lantern panel. To make the wiring convenient, alternate rows run in opposite directions. The copy preserves every lamp state, and the decoding instructions explain the reversal.
The signal names a destination. You do not need nautical knowledge or to count any lights in the illustration.
Each row contains five bits. A bit is the printed digit 0 or 1. Read odd-numbered rows left to right and even-numbered rows right to left.
- 00001
- 10001
- 01000
- 11000
- 00110
- 00100
After choosing the correct reading direction, assign the five positions weights 16, 8, 4, 2, 1 from left to right. Add the weights whose bits are 1. A 0 contributes nothing.
Convert each total to a letter using A=0, B=1, C=2, …, Z=25. The alphabet is ABCDEFGHIJKLMNOPQRSTUVWXYZ. Totals 26–31 would be invalid, but none should appear after correct decoding.
Read the six resulting letters in row order. What destination is signaled? As a separate example, the already correctly oriented row 00101 totals 4+1=5, giving F. It is not a seventh row of the message.
Hint 1 - reveal when you want a nudge
Correct the direction before applying weights. Reversing an even row can move a 1 from a large weight to a small one.
Hint 2 - reveal when you want a nudge
Row 4 is printed 11000 but must be read as 00011. It totals 2+1=3, so its letter is D.
Reveal the solution and explanation
The destination is BRIDGE.
| Row | Oriented bits | Total | Letter |
|---|---|---|---|
| 1 | 00001 | 1 | B |
| 2 | 10001 | 17 | R |
| 3 | 01000 | 8 | I |
| 4 | 00011 | 3 | D |
| 5 | 00110 | 6 | G |
| 6 | 00100 | 4 | E |
Rows 2 and 6 look unchanged when reversed because their bit patterns are symmetrical. They still obey the alternating rule. It is row 4 that makes ignoring that rule visibly fail:11000 totals 24, which would produce Y instead of D.
The zero-based alphabet is equally important. Using A=1 would shift every interpretation and would contradict the supplied example, where a total of 5 means F.
Uniqueness follows at each stage: the row number fixes orientation, the five weights fix a total, and each permitted total fixes one letter. Encoding BRIDGE back into five-bit values and reversing its even rows returns all six printed rows exactly. This check uses the actual digits, independent of any expectation about a harbor destination.
Solve another: The Cabinet of Fifty Mysteries · Browse all 50 cases
