Shanti L. Howard

Click here to see what the problem calls for.

Did you get 1, 5, 13, 27 so far? Yes. How many triangles when there are five levels? 10 levels?

Take a look at the number of triangles when there are five levels and when there are ten levels:


How do you verify your sequence?

The way my kids would probably verify their sequence is by actually working the problem out by using the skill of drawing to enhance their creative side.


Is there a general formula for n levels?

Tn ....T(n-1)


We do not have total proof just yet.



Recognition of the sequence of triangular numbers is useful.

Hint: Count the number of triangles of each size in two parts:
those pointing up and those pointing down.