I got an email recently – fun with numbers. Wouldn’t math have been so different in school had we been taught this along side QED’ing those boring theorems anf cramming multiplication tables?

*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

*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

123456789 x 9 +10= 1111111111

*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

And here’s some more symmetry:

*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

I recently came across a blog Tickled By Life that had a story on how this symmetry got used:

*I tell them the story of German mathematician Gauss, Karl Friedrich (1777-1855) who calculated 1+2+3+…+100 very fast when he was a young boy. By reversing the order from “1+2+3+…+100” to “100+99+98+…+1” and added the two sets together he had every term equaled to 101. There were 100 sets of 101, so he had 10100. But the teacher just wanted one set of “1+2+3+…+100”, therefore the answer was 5050.*

1 + 2 + … + 99 + 100

100 + 99 + … + 2 + 1

_______________________

*101 + 101 + … + 101 + 101*

_______________________

*100 x 101 =10100*

*10100 ÷ 2 =5050*

*This example helps students to see that if we make use of our mathematical knowledge in a creative way we can do wonders.*

Now, let’s play with the alphabet. What does it mean to give 100% ?

Here’s a little mathematical formula that might help answer these questions:

If:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Is represented as:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26.

Then: H-A-R-D-W-O- R- K

8+1+18+4+23+ 15+18+11 = **98%**

And: K-N-O-W-L-E- D-G-E

11+14+15+23+ 12+5+4+7+ 5 = **96%**

But: A-T-T-I-T-U- D-E

1+20+20+9+20+ 21+4+5 = **100%**

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