There are 100 switches labeled from 1 to 100 corresponding to each of the bulbs. 10 persons are asked to report the number of defective bulbs they had found, such that the 1st person is allowed to check all the bulbs while the 2nd person is allowed to check bulbs corresponding to switches labeled 2,4,...,100 and so on, and the 10th person is allowed to check bulbs corresponding to switches labeled 10,20,...,100.

Each person reported the same number of defective bulbs. Also note that the number of defective bulbs can increase or remain the same between two consecutive testings and there is at least one defective bulb. Find the following just after the 10th person finished his test.

1) What can be the minimum number of defective bulbs? What are the defective bulbs in this case?
2) What can be the maximum number of defective bulbs? What can be the maximum number of bulbs that can be found to be defective?

(In reply to Two solutions for Q 1. by rod hines)

I found four solutions for Q 1, with the same minimum number of defective bulbs, two.  I wonder, though, if I made an error. Well, here is the result that I had found, with the inspection as one of the following:

• Bulb #90 and sometime after the 2^nd person and before the 4^th person, bulb #56.
• Bulb #90 and sometime after the 2^nd person and before the 5^th person, bulb #96.
• Bulb #72 and sometime after the 2^nd person and before the 5^th person, bulb #70.
• Bulb #70 and sometime after the 2^nd person and before the 3^rd person, bulb #72.

I did find my error: bulb #90 and #96 both would be found defective by inspector 6 and undiscovered as defective by inspector 7. And, as pointed out by Charlie in the later post:

Bulb #56 and sometime after the 2^nd person and before the 3^rd person, bulb #90.

Edited on December 13, 2008, 3:39 pm

Posted by Dej Mar on 2008-12-12 21:14:36