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Defective Bulbs (Posted on 2008-12-12) Difficulty: 3 of 5
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?

No Solution Yet Submitted by Praneeth    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Two solutions for Q 1. | Comment 4 of 5 |
(In reply to re: Two solutions for Q 1. by Dej Mar)

The following table shows: bulb initially burned out, second bulb to go out, and step just before which the second bulb goes bad:

56  90  3
70  72  3
72  70  3
72  70  4
72  70  5
90  56  3
90  56  4

So it can be 56 and 90 in either order or 70 and 72 in either order, with choice of failure point dependent on the order.

DEFDBL A-Z
FOR b1 = 1 TO 100
FOR b2 = 1 TO 100
FOR sw = 2 TO 10
 good = 1
 FOR p = 2 TO 10
  ct = 0
  IF b1 / p = INT(b1 / p) THEN ct = 1
  IF sw <= p THEN
   IF b2 / p = INT(b2 / p) THEN ct = ct + 1
  END IF
  IF ct <> 1 THEN good = 0
 NEXT
 IF good THEN PRINT b1; b2; sw
NEXT
NEXT
NEXT


  Posted by Charlie on 2008-12-13 12:37:35
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