Page 98 - NUMINO Challenge_C1

Basic Concepts Rules of Number Arrangements in Square Patterns

When arranging numbers in a square pattern following a certain rule, you
can find a pattern in the numbers of each column, row, and diagonal.

Column 1 2 3 4 5
Row

1 1 4 9 16 25 Rule: 1, 4, 9, 16, 25,

2 2 3 8 15 24 1 12 23 34 45 5

3 5 6 7 14 23

4 10 11 12 13 22

5 17 18 19 20 21

Rule: 1, 2, 5, 10, 17, Rule: 1, 3, 7, 13, 21,
1357 2468

Example Use the pattern in the numbers below to find the numbers in the
8th row, 1st column, and 9th row, 9th column.

Column 1 2 3 4 5
Row

1 1 4 9 16 25

2 2 3 8 15 24

3 5 6 7 14 23 զ

4 10 11 12 13 22

5 17 18 19 20 21

զ

Class Notes

The number added to each number of column 1 increases by .

Since the number of row 8, column 1 is the th

number of column 1, it is

1 (1 3 5 ).

The number of row 9, column 9 is on the diagonal. List the diagonal numbers and
find a pattern, and then you will see that the number added to each term increases
by .
Since the number of row 9, column 9 is the th number of the diagonal, it is

1 (2 4 6 ).

95Rules and Numbers