Question

Світло на дев’ятому поверсі можна вмикати та вимикати кожним з п’яти вимикачів незалежно один від одного. Вимикачі розміщено на першому поверсі. Один вимикач не працює. Електромонтер може в будь-якому порядку вмикати і вимикати вимикачі. Як він повинен це робити, щоб електрик на дев’ятому поверсі з’ясував , який вимикач не працює?

Answer 1

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Answer 2

Understanding the Problem

The problem states that there are five switches on the first floor that control the lights on the ninth floor. Each switch can be turned on or off independently of the others. However, one of the switches is not working. The goal is to determine which switch is not working by using the switches on the first floor.

Solution

To determine which switch on the first floor controls the lights on the ninth floor, the electrician can follow these steps:

1. Turn on the first switch and leave it on for a few minutes. 2. Turn off the first switch. 3. Turn on the second switch. 4. Go to the ninth floor and observe the lights. - If the lights are on, the second switch controls the lights on the ninth floor. - If the lights are off, proceed to the next step. 5. Turn off the second switch. 6. Turn on the third switch. 7. Go to the ninth floor and observe the lights. - If the lights are on, the third switch controls the lights on the ninth floor. - If the lights are off, proceed to the next step. 8. Turn off the third switch. 9. Turn on the fourth switch. 10. Go to the ninth floor and observe the lights. - If the lights are on, the fourth switch controls the lights on the ninth floor. - If the lights are off, proceed to the next step. 11. Turn off the fourth switch. 12. Turn on the fifth switch. 13. Go to the ninth floor and observe the lights. - If the lights are on, the fifth switch controls the lights on the ninth floor. - If the lights are off, the first switch controls the lights on the ninth floor.

By following this process, the electrician can determine which switch on the first floor controls the lights on the ninth floor. If the lights are on after following the steps, it means that the last switch turned on controls the lights. If the lights are off, it means that the first switch turned on controls the lights.

Note: This solution assumes that the switches on the first floor are labeled or numbered for easy identification. If the switches are not labeled, the electrician may need to label them before following the steps.

I hope this helps! Let me know if you have any further questions.