A box contains
10 red pills
5 blue pills
12 yellow pills.


What is the least number of pills one must extract to ensure at least
1. one blue pill?
2. two blue pills?
3. one blue and one yellow?
4. two blue and one yellow?
5. two blue and two yellow?
6. at least one of each color?
7. at least 3 of each color?

A box contains
10 red pills
5 blue pills
12 yellow pills.

What is the least number of pills one must extract to ensure at least
1. one blue pill?
2. two blue pills?
3. one blue and one yellow?
4. two blue and one yellow?
5. two blue and two yellow?
6. at least one of each color?
7. at least 3 of each color?


Soln:
1. one blue pill?
Ans: The worst case is if we pick all 10 red pills and 12 yellow pills and then only pick the first blue pill. So the least number of pills to ensure that atleast one blue pill is taken is 23.

2. two blue pills?
Ans: Similar to first question. Since now we need two blue pills. Thus the answer is 24.10 red pills + 12 yellow pills + 2 blue pills

3. one blue and one yellow?
Ans: 10 red pills + 12 yellow pills + 1 blue = 23

4. two blue and one yellow?
Ans: 10 red pills + 12 yellow pills + 2 blue = 24

5. two blue and two yellow?
Ans: 10 red pills + 12 yellow pills + 2 blue = 24

6. at least one of each color?
Ans: 10 red pills + 12 yellow pills + 1 blue = 23

7. at least 3 of each color?
Ans: 10 red pills + 12 yellow pills + 3 blue = 25

Silly question, but arent the least number of pills, at least for question 1, one ? I.e. the first pill you pick is the blue one ??

So what is wrong with my approach on #3 then: 10 Red + 5 Blue + 1 Yellow = 16 ?

Yeah in order to get least number of required ones , we need to maximise the wrong ones. 23 is right !

So.. for 6 and 7 ..

At least one of each color .. since 5 is the lowest number we choose 10R 12Y and 1B ? I didn't quite get this.

I think question should ask "MAX or Most" rather than "Least", for worst case scenario.
What is the max number of pills one must extract to ensure at least ?

One of my friend was asked a similar question in a job interview and he replied - "One" - interviewer asked how - and he said that "I am lucky so i will get it in first pick and would not wait for X picks (x=real solution))
Interviewer liked his boldness and presence of mind. And he was selected.

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Hope it helps.
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For such questions you should consider the worst case scenario. The worst case scenario for question 3 (at least one blue and one yellow) would be if we pick all 10 red pills and all 12 yellow pills. In such case we still won't have at least one blue and one yellow. Next, pick however, would give us blue pill, so we would have at least one blue and one yellow. So, the correct answer is 10 + 12 + 1 = 23.

Check other Worst Case Scenario Questions in our Special Questions Directory.

Hope it helps.
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