# Bogglers

#### Reason, Rhyme & 'Rithmetic

By Scott Kim|Friday, November 4, 2005

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 (www.ditd.org/public) riffed on classic puzzling themes. The kids are back, this time with a set of original challenges.

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.

ELEMENTARY POETRY

 ELEMENTS       hydrogen 1helium 2lithium 3beryllium 4boron 5carbon 6nitrogen 7oxygen 8fluorine 9neon 10sodium 11magnesium 12aluminum 13silicon 14phosphorus 15sulfur 16chlorine 17argon 18potassium 19calcium 20scandium 21titanium 22vanadium 23chromium 24manganese 25iron 26

A. [Easy]

Our teacher gave a talk to our science class today—

The kids in class were Marty, Sue, Christopher, and Jay.

He assigned each a report, between 10 and 15 pages,

About a simple element that he has known for ages.

The lightest one of all he promised would be Marty's;

Christopher got a gas that fills balloons at parties.

The others he assigned are common in the air.

Jay's was heavier than Sue's, but no one seemed to care.

Their atomic numbers have 18 as their sum.

Now, which elements are these, and which kid has which one?

B. [Challenging]

The teacher gave us five more chemical elements to explore

Their atomic numbers totaled 68, no more.

No two atomic numbers differ by less than 5.

One is number 8 (the element helps keep you alive).

Two of the atomic numbers differ by exactly 10,

And one's three times another, so grab pencil, chalk, or pen.

Can you find all five? Let's see if you can pass.

I'll give you one more hint: The lightest's not a gas.

The answers fall within the first 26 elements of the periodic table. Those elements are listed at right, by atomic number, to help you out. Elements in blue are gases.