Problem of the Week 21

Suppose the numbers from 1 to 30 are arranged in consecutive order.  How many different pairs of numbers may be selected if there are at least three numbers between the chosen numbers?

 

Alternate Problem 21

Three black and three white beads are arranged on a string, forming a circular bracelet.  How many different color patterns are possible?

 

Extension Problem 21

Suppose you have a three by four block of twelve postage stamps.  You wish to give for stamps to a friend, all joined together with no stamp attached at the corner only.  For example, you could give a combination of ABCD, or BCFG, or ABCF, and so on.  How many different combinations of the four stamps are possible?

 

A B C D
E F G H
I J K L