The Alchemists Pressure Valve
Adjust the HEAT and STEAM levels to reach the SAFE state. The SAFE output must be true only if HEAT is active and STEAM is not, but neither being active simultaneously.
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The truth table
Inputs on the left, the output on the right. A circuit solves the puzzle when it reproduces every row.
| HEAT | STEAM | SAFE |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
What the table tells you
- SAFE is 1 in 2 of the 4 rows, a balanced function, which is what XOR-like and single-input-like rules look like. Every input matters: for each one there is a row where flipping it changes SAFE.
The smallest known circuit: 4 gates
As a formula, one line per output:
SAFE = ((HEAT AND NOT STEAM) OR (NOT HEAT AND STEAM))
As a netlist, in the order you would wire it. Each g is one gate; the last line says which signal drives the output.
g1 = HEAT NAND STEAMg2 = HEAT NAND g1g3 = STEAM NAND g1g4 = g2 NAND g3SAFE = g4
The search checked every circuit with fewer gates and none matches the table, so 4 is the true minimum for the allowed gate set. Gates that do not feed an output are never counted.
Leaderboard for the day
Nobody posted a result on the day. The circuit above is the reference.