FUN WITH NUMBERS

10 x 10 plus 11 x 11 plus 12 x 12 = 365

13 x 13 plus 14 x 14 = 365


The values 10 x 10 through 14 x 14 are the only consecutive products that give identical results when arranged as above. By coincidence, the results are the number of days in a year.

FUN WITH NUMBERS

There is an infinite number of numbers that have the same value whether added or multiplied. They follow this pattern:

3 + 1-1/2 = 3 x 1-1/2 = 4-1/2

4 + 1-1/3 = 4 x 1-1/3 = 5-1/3
5 + 1-1/4 = 5 x 1-1/4 = 6-1/4
...

1000 + 1=1/999 = 1000 x 1-1/999 = 1001-1/999
etc.

However, there is only one integer that can be added to itself and multiplied with itself with the same result:

2 + 2 = 4 and 2 x 2 = 4

FUN WITH NUMBERS

123456787654321

is

11,111,111

multiplied by itself.

FUN WITH NUMBERS

Mathematics, too, has arrangements
that could be called palindromes.
For example:

21978 x 4 = 87912
10989 x 9 = 98901

There are more complex examples of reversal,
mixing addition and multiplication.
For example:

9 + 9 = 18 ..... 81 = 9 x 9
24 + 3 = 27 ..... 72 = 3 x 24
47 + 2 = 49 ..... 94 = 2 x 47
497 + 2 = 499 ..... 994 = 2 x 497

SYMMETRY IN NUMBERS

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 =
123456787654321
111111111 x 111111111 =
12345678987654321