# Bogglers

#### Get ready to go back to school again. In our November 2004 issue, gifted students from the Davidson Institute for Talent Development's Young Scholars Program riffed on classic puzzling themes. The kids are back, this time with a set of original challenges.

By Scott Kim|Tuesday, January 17, 2006

LINEAR THINKING

Each paragraph below describes at least one diagram made of straight lines and a specific number of points of intersection where the lines cross. Can you draw the diagrams? (Lines cannot be cut short to make the diagrams work.)

A. [Easy] The figure at right can be described as follows: There are four lines. Each line has two or three points of intersection. Each point is an intersection of two lines. Can you draw three other figures that fit this description?

B. [Easy] There are four lines. Each line has two or three points of intersection. Each point, except one, is an intersection of two lines. (There are two solutions.)

C. [Challenging] There are six lines. Each line has two or three points of intersection. Each point, except one, is an intersection of three lines. (There is one solution.)

D. [Challenging] There are five lines, and each line has either two or three points of intersection. The total number of points where two lines intersect is equal to the number of points where three lines intersect. (There is one solution.)

E. [Difficult] There are seven lines. Each has two or three points of intersection. The number of points where two lines intersect is equal to the number of points where three lines intersect. (There are two solutions.)

PYRAMID SCHEME

A. [Easy] Jill wants to arrange 21 numbers in the pyramid shown below so that the numbers in each row add up to 17. Which blocks must go in each row? (To get you started, 17 must be the top block; the next row could contain 2 and 15, or 5 and 12.) There are many solutions.

B. [A bit harder] Arrange the same blocks in the same pyramid so that the sums of the rows, starting from the top, are 12, 14, 16, 18, 20, and 22. What blocks must go in each row? Again, there is more than one solution.