傑克，這真是太神奇了

同事傳來了一封有關數字的郵件，讓我想起了國中時鍾老師順口提到的一個簡易乘法。當時因為覺得很特別而且邏輯又清楚，所以一直記到現在。就是求以五為尾數的數字平方值時，只要將前方數字ｘ前方數字＋１然後尾數放上25就行了。

eg,

15 x 15 = 1 x 2 +尾數 25 => 2 25
25 x 25 = 2 x 3 +尾數 25 => 6 25

其餘類推
35 x 35 = 1225
45 x 45 = 2025
55 x 55 = 3025
　　．
　　．
　　．
　　．

同事寄來的郵件原文如下：

3 x 37 = 111
6 x 37 = 222
9 x 37 = 333
12 x 37 = 444
15 x 37 = 555
18 x 37 = 666
21 x 37 = 777
24 x 37 = 888
27 x 37 = 999

Nice one:
111.111.111 x 111.111.111 = 12.345.678.987.654.321

Trapeze:
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111

another Trapeze:
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

and another one:

0 x 9 + 8 = 8
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
987654321 x 9 - 1 = 8888888888
9876543210 x 9 - 2 = 88888888888

數字真的很特別！