Page 90 - NUMINO Challenge_B1

Basic Concepts Rules for the Difference Between the Number of
Stones

Arrange white and black stones in a square. Then find the difference
between the number of white and black stones by drawing a table.

Stones Squares 1 1 2 2 3 3 4 4 5 5

Number of White Stones 0 3 3 10 10

Number of Black Stones 1 1 6 6 15

Difference 12345

In the picture above, there are 3 more black than white stones when the
stones are placed in a 3 3 square. There are 4 more white than black
stones when the stones are placed in a 4 4 square.

Example Stones are placed in the following order. Find the difference
between the number of white and black stones when they are
arranged in a 6 6 square.

2 2 square 3 3 square 4 4 square

Class Notes

Find the difference between the number of white and black stones in each arrangement,
and write them in the following table.

Stones Squares 2 2 33 44 55
9(3 3)
Number of White Stones 4(2 2)

Number of Black Stones 1(1 1)

Difference 3

The difference between the number of white and black stones in each square is:

3, , , . It starts from 3 and increases by .

Therefore, the difference between the number of white stones and black stones when

they are arranged in a 5 5 square is , and the difference is when they are

arranged in a 6 6 square.

87Rules for Shapes