What is the fewest number of beads I must pick?

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?

This is an extension of pigeon hole problem .

Metro Eye: Do not get distracted by total number of beads or number of beads of each color.

Number of different colors, k = 5
Required number, p = 5
Fewest number of tries =  k*(p-1)+1 =  5*4+1 = 21

At least 21 beads needs to be picked up to be absolutely sure there are 5 beads of same color.




  

How many different amounts of postage?

I have four 3 cents stamps and three 5 cents stamp using one or more of these stamps. Using one or more of these stamps. How many different amounts of postage can I make?

Four 3 cents stamps can be used in 4 different ways (using 1 stamp, 2 stamps, 3 stamps and 4 stamps at a time)

Similarly Three 5 cents stamps can be used in 3 different ways.
So both stamps together can be used in 4*3 = 12 different ways. 
=> Total different ways = 4+3+12=19 

19 different amounts of postage can be made using the stamps.