Index Of Fun

Today's Puzzles

1. 1.    Sudoku

2. 2.    Wonder Word

3. 3.    Daily Crazy Quiz

4. 4.    Brain Teaser Contest

5. 5.    Themed Crossword

6. 6.    Word Jumble

7. 7.    Cryptogram

8. 8.    Kakuro

9. 9.    Word Search

10. 10.  Word Crunch

11. 11.  Word Square Puzzle

12. 12.  JigSaw

13. 13.  Anything Puzzles

14. 14.  All Our Daily Puzzles

Puzzle Zone Navagation

What's New?
Topic Of The Day
Interactive Puzzles
IQ Tests and Quizzes
Daily Videos
Jigsaw Puzzles
Word Puzzles
Sudoku Zone
Maze Zone
Mahjong Zone
"GRY" Puzzle
Trivia Zone
Daily Education
Ultimate IQ Test
Brain Bashers

    Our Fun Sites

A Fun Zone
A Puzzle Zone
A Game Zone
Top 100 Game Sites
Puzzle Store
Brain Teaser Archives
Fun Game Sites
A Free Zone

Daily Brain Teaser / Puzzle
November 25, 2006
Previous Days Teaser -- Want More? -- Next

Trevor the travel agent has a map of Europe on which every major town is joined to the town nearest to it. The distances between towns are always different, when measured sufficiently accurately. What is the largest number of other towns to which any one town can be connected?

VIEW SOLUTION BELOW

If you see this, you may need to update your browser.

THE SOLUTION

Five. Suppose that it were possible for one town to be connected to six other towns. It is connected to one other town which is the closest town to itself. The other five connections are all to towns for which it is the closest other town. But if six points are arranged round a central point, the central point can only be equal closest to the other points, when they are arranged at the centre and vertices of a regular hexagon. As soon as the distances are adjusted, even very slightly, to make them all different, one of the ring of points will be nearer to another point than it is to the centre of the hexagon, contradicting the information given.