Bogglers

By Scott Kim|Sunday, July 25, 2004

 

 

 

It’s a small world

You meet a stranger at a party. After talking for a few minutes, you find that you know someone in common. Is this a mere coincidence? Research suggests that any two people on Earth can be linked by a surprisingly small chain of intermediary acquaintances—an observation popularly known as the small-world effect.


 

I’m looking for my missing link

The small-world effect applies to seemingly unrelated words as well as to people. Tony McCaffrey, creator of the children’s television show ImagiNation, noticed that for almost any two words, like needle and lightbulb, you can almost always find two intermediate words that link one to the other. For instance, part of a needle is an eye, an eye sees light, and light is produced by a lightbulb. This phenomenon has a scientific pedigree: In 2002 Adilson Motter and his colleagues at Arizona State University found that any two “root” words in a thesaurus can be linked, on average, by two other related words. Fill in the missing links to connect the eight pairs of words that appear below. Each pair of adjacent words must be strongly related in some obvious way. These puzzles have multiple answers—the connections are limited only by your imagination. For more missing-links puzzles, see imaginationchallenge.com.

1. NEEDLE EYE LIGHT LIGHTBULB

2. CLOCK ______ ______ LOBSTER

3. STYROFOAM_____ ______ PRAYER

4. TREE _____ ______ PIPE

5. EGG _____ ______ TUNNEL

6. CEMENT _____ ______ STAR

7. LICENSE _____ ______ CABBAGE

8. PEPPER _____ ______ PIANO


Won’t you be my neighbor?

In 1998 mathematicians Duncan Watts (now at Columbia University) and Steven Strogatz at Cornell University published an analysis of the small-world phenomenon, which has potential applications in fields as varied as economics, epidemiology, and neurology. Here’s the idea in a nutshell: The characters above, linked by red lines, form an orderly “caveman” network. Like cavemen, who would have known only those nearby, people in this network are connected only to their neighbors.

1. Looking at only the red connections, how many steps does it take to get from Ann to Zeke?

2. Which individual is separated from Ann by a larger number of connections?

3. Which two people are separated by an even larger number of connections?

The average number of connections between people in a caveman network is high. But throw in a few long-distance connections (blue lines above), and this average shortens dramatically.

4. How many connections does it take to get from Ann to Zeke, using both red and blue lines?

5. Considering both red and blue lines, which two people are five connections away from Ann?

6. Now what is the largest number of connections separating any two people in the network?

Click here for Bogglers Solutions

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