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## 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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