Maths with attitude

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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