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Eight light bulbs numbered 1 through 8 are arranged in a circle as shown above. The bulbs are wired so that every third bulb, counting in a clockwise direction, flashes until all bulbs have flashed once. If the bulb numbered 1 flashes first, which numbered bulb will flash last? – OGQR 2020 Question #102 with Solution

OGQR 2020: Question No. 102

Eight light bulbs numbered 1 through 8 are arranged in a circle as shown above. The bulbs are wired so that every third bulb, counting in a clockwise direction, flashes until all bulbs have flashed once. If the bulb numbered 1 flashes first, which numbered bulb will flash last?

Source OGQR 2020
Type Problem Solving
Topic Number Properties
Sub-Topic Basic
Difficulty Easy – Medium

Solution

Given

In this question, we are given

  • Eight light bulbs numbered 1 through 8 are arranged in a circle, as shown in the diagram.
  • The bulbs are wired so that every third bulb, counting in a clockwise direction, flashes until all bulbs have flashed once.
  • The bulb numbered 1 flashes first.

To Find

We need to determine

  • The number of the bulb that will flash last.

Approach & Working

As every third bulb is flashing, starting from bulb 1, we can determine the next bulbs as follows

  • First: Bulb 1
  • Second: Bulb 4
  • Third: Bulb 7
  • Fourth: Bulb 2
  • Fifth: Bulb 5
  • Sixth: Bulb 8
  • Seventh: Bulb 3
  • Eighth: Bulb 6

As we can see, all the eight bulbs are flashing at least once, and the last one to flash is bulb 6.

Hence, the correct answer is option D.

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