How to solve Worst Case Scenario Problems

What are worst-case scenario problems? Why do we need to solve them? These are some of the questions that pop up in our head when we read the title.

Worst Case Scenario problems are a genre of problems that appear in various math competitions like Math Kangaroo, MOEMS (math olympiad for elementary and middle schools), AMC8, Math Counts, GMAT etc. They can be solved by logical reasoning. If you've solved math competition problems then you might have seen questions like

"A box has a variety of red, blue and green colored socks. You have your eyes closed. What is the least number of socks you need to remove from the box to be certain that you have a pair of socks of the same color?"

These questions fall under the Worst Case Scenario Problems. They want the least number of items picked and also be certain to get what you want. So we want to be covered for the worst case that can happen but with the least number of tries.

So let's take a few questions and see how we can work it out. Nothing better than solving by examples right?

Question 1:

"A box has a variety of red, blue and green colored socks. You have your eyes closed. What is the least number of socks you need to remove from the box to be certain that you have a pair of socks of the same color?"

Question 2:

A box has 4 red socks, 5 blue socks, and 7 green socks. Again you have your eyes closed. What is the least number of socks you need to remove from the box to be certain that you have 2 pairs of same colored socks?

Question 3:

A bowl has 100 pieces of colored candy. 48 green, 30 red, 12 yellow and 10 blue. They are all wrapped in foil, so you do not know the color of any piece of candy. Write the least number of pieces you must take to be certain that you have at least 15 pieces of the same color? – source MOEMS (Math Olympiad for Elementary and Middle Schools) competition

And at last the Summary on how to solve Worst Case Scenario Problems in general:

So that's how Worst Case Scenario Problems are solved. Hope you got the hang of it.

Try this problem and post your answer in the comments section below

"Tucker has a jar containing 4 green and 5 blue marbles. What is the minimum number of marbles Tucker needs to remove from the jar, without replacement, to guarantee that he has at least four marbles of the same color among those removed?" – source Math Counts 2016 Sprint Round School competition.

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