Programming on the Wall

Currently, I'm learning to perform algorithm analysis using Big-O notation. In one resource I found the following problem: You just dropped a box of glass toys and  n  toys in the box broke in half. You'd like to match the halves of the toys so that you could glue them together, but the only way to tell whether two halves belonged to one toy is to physically pick up the two pieces and try to fit them together. Express how long this matching process will take in terms of  n . The answer given is n^2 (n squared) with the following explanation:  You have to compare every piece with every other piece. If you have 1 toy and it breaks in half, you have 1 comparison to make. If you have 2 toys and they both break in half there are 4 pieces and you have to do 6 comparisons. If you have 3 toys, there are 6 pieces and you have to do 15 comparisons. If you have  N/2  toys, you have  N  pieces and you have to do N-1 + N-2 + N-3 + ... + 1 =(N)(N-1)/2...

On Monday I began working through a Discrete Math textbook in preparation for some courses I'll be taking in January. There was a beautiful logic problem in Chapter 1, apparently created by Einstein. This is one version of it: Five men with  different nationalities and with different jobs live in  con secutive houses on a street. These houses are painted  dif ferent colors. The men have different pets and have   dif ferent favorite drinks.  Determine who owns a zebra and  whose favorite drink is mineral water (which is one of the  favorite drinks) given these clues:  The Englishman lives  in the red house.  The Spaniard owns a dog.  The Japanese  man is a painter.  The Italian drinks tea.  The Norwegian  lives in the first house on the left.  The green house is  immediately to the right of the white one. The photogra pher  breeds snails.  The diplomat lives in the yellow house. ...