Correctly explaining and solving a problem


New Member
My friend was helping her 9 year old daughter with her math and she asked me for help with the following problem: A bag contains 500 beads, each of the same size, but in 5 different colors. Suppose there are 100 beads of each color and I am blindfolded. What is the fewest number of beads I must pick to be absolutely sure there are 5 beads of the same color among the beads I have picked blindfolded? Explain your answer in detail.

I solved the problem in the following way: I looked at the worst case scenario. I said okay if I selected 4 beads of color1, 4 more beads of color2, ... 4 more beads of color5 then the next bead I select will give me 5 beads of one of the colors. This gives me (4 * 5 +1) = 21. That I believe is the answer. I'm sure there is a better way to solve the problem. Can you tell me the proper way to solve it so that I can explain it to my friend's 9 year old daughter? She was given this and other word problems for practice in preparation for a math contest. Can you direct me to a resource that might help explain stategies for solving various kinds of math word problems. These problems are not in her text book.


TS Contributor
There are many different ways to solve math problems and not just the so-called "right" way. Your "worst-case" approach was simple, and it allowed you to arrive at the correct answer.

Maybe if you explain it from the standpoint of purposely avoiding the 5th bead of the same color by selecting 4 from each color, then on the 21st draw you are forced to pick the 5th (there's no way to avoid it any longer).