Enter Puzzle Values
Example Data Table
| Case | Bulbs | Power | Heat Time | Delay | Expected Clues |
|---|---|---|---|---|---|
| Classic puzzle | 3 | 60 W | 90 s | 20 s | Lit, warm, cold |
| Slow inspection | 3 | 40 W | 60 s | 90 s | Weak warm clue |
| Advanced timing | 5 | 75 W | 240 s | 15 s | Lit, cold, warm bands |
Formula Used
Input energy: E = P × t
Stored heat: Q = E × efficiency
Temperature rise: ΔT = Q ÷ (m × c)
Cooling model: ΔTvisit = ΔT × e-delay ÷ τ
Required time gap: gap = sensitivity ÷ temperature rate + 2 × clock error
Guess chance: probability = 1 ÷ n!
How to Use This Calculator
Enter the number of bulbs and switches in the puzzle.
Add bulb power, heating time, cooling delay, and clock error.
Set the thermal values if you want a stricter physics model.
Press the calculate button to see the result above the form.
Use the schedule table to assign switch actions before observation.
Download the CSV or PDF file for saving your result.
A Physics View Of The Puzzle
The clocks and light bulbs puzzle looks simple. It becomes rich when timing and heat are measured. A switch can leave three clues. A bulb may be on, warm, or cold. The calculator turns those clues into a planned test.
Why Timing Matters
The first switch heats a bulb for a set time. Then it is turned off. A second switch stays on during inspection. A third switch remains off. When the door opens, the lit bulb belongs to the second switch. The warm dark bulb belongs to the first switch. The cold dark bulb belongs to the unused switch.
Heat As Information
A bulb stores part of the electrical energy as heat. The stored heat raises its temperature. Cooling lowers that extra temperature before observation. Better bulbs, larger glass, drafts, and delays all change the clue. The calculator estimates this clue with power, mass, heat capacity, efficiency, and cooling time.
Clock Error And Risk
Real clocks are never perfect. A short timing error can make two warm bulbs feel the same. This matters when many switches are tested with different heating times. The tool subtracts a timing safety allowance. It then estimates how many warm bands remain distinct.
Using More Bulbs
A larger puzzle needs more unique states. One bulb can be lit. One bulb can stay cold. Other bulbs can use different heating durations. The spacing between those durations must be large enough. Each warm band should exceed the touch sensitivity. Otherwise the mapping is not reliable.
Interpreting Results
A solvable result means the planned clues are separated enough. It does not prove the room is safe. Do not touch live circuits. Use noncontact methods where possible. Treat the result as a logic and learning model, not an electrical safety certificate.
Study Benefits
This puzzle teaches energy, heat transfer, exponential cooling, factorial guessing, and experimental design. It also shows why physical clues need tolerances. A correct plan needs more than clever logic. It needs measurable differences, controlled time, and clear observations.
Common Mistakes
Many wrong solutions ignore cooling. Others assume every warm bulb feels unique. Small delays can erase weak clues. Good plans leave generous time gaps. Record observations before making decisions.
FAQs
What is the classic light bulbs puzzle?
It is a logic puzzle with switches outside a room. Bulbs are inside. You use light and heat clues to match switches to bulbs with limited visits.
Why does heat matter in this puzzle?
A bulb can stay warm after it is turned off. That warmth creates a second clue besides being lit or cold.
Can this calculator handle more than three bulbs?
Yes. It estimates whether extra timed warm bands can separate more switches. The result depends on power, time, cooling, and sensitivity.
What does clock error mean?
Clock error is the possible timing mistake. Larger error needs wider timing gaps, or warm clues may overlap.
What is the cooling time constant?
It controls how fast the bulb loses extra heat. A larger value means the bulb cools more slowly.
Is touching a bulb always safe?
No. This page is a physics model only. Do not touch live or unsafe electrical parts. Use safe observation methods.
Why is the random guess chance so small?
Every switch-to-bulb mapping is a permutation. With n bulbs, there are n factorial possible mappings.
Can I export my result?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a quick report.