Triangle Magic

55. Triangle Tribulations

Triangle Magic

"Now what?" says Anita, staring at the triangle the three of you have formed from the cubes (see "Triangle Tribulations"). "We are still stuck in the fourth dimension. This just doesn't add up."

The phone rings again, and you answer.

"I forgot to tell you something," says Three. "You need to number each block."

"No problem. They go from 1 to 36."

"No, no! You have to make everything add up," says Three. "Once they are stacked in a triangle, write '1' on the top cube. Then, on each cube below, write the sum of the cubes above it. Each cube in the second row has a '1' over it, so write '1' on each second-row cube."

"In the third row, write '1' on the first (left) cube," Three continues. "The center cube has two '1's over it, so write '2.' The third cube has only one '1' over it, so write '1.' Keep on going like that, and you will be amazed by what turns up!"

What's so amazing about those numbers?

TRY IT!

Label each cube (or square) with the sum of the cubes in the row above and see what pattern turns up.

You will need:

• pencil
• a sheet of paper with a drawing of 36 squares arranged in a triangle

Thirty-six square tiles arranged to form a triangle.

What to do:

1. Write "1" in the top square.
2. Write "1" in each square in the second row.
3. Write "1," "2," and "1," in that order, on the cubes in the third row.
4. Number each square in the fourth row with the sum of the squares above it. You should get "1," "3," "3," and "1," in that order.
5. Continue numbering the rows in this way until you have numbered all the squares.
6. When you are finished, look for number patterns along rows and diagonals. Try adding the numbers along each row to see what you get.

NEXT: Pascal's Patterns