Some interesting interview puzzles

1.You have 7 balls. One weighs more than the others (not significantly). You have a scale, like the scales of justice. Describe how to find the weighted ball only using the scale twice.

Ans: First select any 4 balls randomly, weigh them 2 vs 2.

If they are equal select 2 more randomly and weigh them 1 vs 1.

If they are equal, then the remaining ball is the heavier one.

If the 2 weighed once are not equal, heavier one is found then.

If the first 4 balls don’t weigh equal, weigh the 2 balls from side which went down.

This should identify the heavier ball by using the scale twice only.

 

2. If you have a vacant field and add one flower and the number of flowers doubles everyday and at the end of 45 days, the field is full, on what day is the field half full?

Ans: Since the field is full on 45th day, it must be half full on 44th day. When all the flowers doubled after 44th day, hall became full on 45th day.

 

3. There are 3 non-transparent buckets with FALSE labels ‘Red’, ‘Blue’ and ‘Red+Blue’ on them. There are equal numbers of balls in all 3 buckets; one of them has only red, one of them has only blue and other one has both blue and red balls. How many minimum numbers of attempts are required to correct the labels?

Ans: This is not a probability question. Only one ball needs to be picked up from bucket with ‘Red+Blue’ label. If that ball is ‘Red’ then that bucket should contain all the red balls. Since the label is a false label. Now bucket with ‘Blue’ label can be either ‘Red’ or ‘Red+Blue’, but we already know ‘Red’ bucket so it must be ‘Red+Blue’ and then remaining bucket must be corrected with ‘Blue’.

Vice versa if the ball picked up is ‘Blue’ then that bucket is ‘Blue’. ‘Red’ bucket is ‘Red+Blue’ and ‘Blue’ bucket is ‘Red’.

4. You have 3 buckets which can carry 10, 7 and 3 liters each. You have 10 liter of water. Divide the water as 5 liters in 2 buckets.

Ans:

10  7   3

———

10  0   0

3    7   0

3    4   3

6    4   0

6    1   3

9    1   0

9    0   1

2    7   1

2    5   3

5    5   0

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