Interesting Pattern

Have you ever noticed this?

11^2 = 121

111^2 = 12321

1111^2 = 1234321

11111^2 = 123454321

...

111111111^2 = 12345678987654321

1111111111^2 = 1234567900987654321

and so on.

edit : taken from the book Math Wonders to Inspire Teachers and Students.

How true is this?

When I was bored enough during maths lesson, I jotted down some prime number and find something rather surprising. Prime number that is larger or equal to 7 can be re-represented as the sum of three prime numbers. in short, d = a+b+c where a,b,c and d are prime number and d≥7.

Some example up to prime number that is less than 100 would be :
7=2+2+3
11=2+2+7
13=3+3+7
17=5+5+7
19=7+7+5
23=11+5+7
29=23+3+3
31=23+3+5
37=31+3+3
41=31+5+5
43=31+5+7
47=37+5+5
53=43+5+5
59=53+3+3
61=31+13+17
67=61+3+3
71=61+5+5
73=67+3+3
79=73+3+3
83=73+5+5
89=79+5+5
97=41+37+19

Enough of spamming out of the blue.

Thanks to Mr Chew for correcting the mistake.

A Quiz

There is a frog fall inside a 30 meter deep well. The frog can climb 3 meter per day and drop 2 meter per night. Assuming the frog fall on the beginning of the day, how many days needed for the frog to get out of the well.

Pascal triangle and number 11

When I was playing with number 11, I find a rather familiar number pattern for 11^x
we all know that 11^2 = 121 and 11^3 = 1331
121 and 1331 remind me of the polynomial (a+b)^x which leads me to pascal triangle.



Look at the number rows above. The first represent 11^0 which is 1, the second represent 11^1 which is 11 and soon on.
does this mean that 11^5 = 15101051? of course not. It should be calculated this way.


So, the answer is 161051

This method could be applied for 11^x for any value of x due to the nature of no.11

11 = 10+1

Just replace the x with 10 and the y with 1, we will get



since will always be one,




notice that can be derived from pascal triangle.

The last digit of 11^x will always be 1 when the second last will always be the last digit of x

edit: I just realised that the long equation is being cut. Since it does not affect that much, I'll just leave it that way.


last edited on : 15th of May 2010

Subtraction problem

Consider this subtraction problem

1241
- 587

Most people won't like to do this in their head (or even paper)

This subtraction problem could be simplified by subtracting 600 instead of 587

1241-600 = 641

But, we have subtracted too much, 13 (600-587) too much.
So we add the "missing" 13 to the 641 we have. And we get the answer which is 654.

End of Chapter 0

* If there is a positive feedback, I'll post more of this.

Tips on fast mental calculation

Hey guys, I just bought a book on mental calculation. It is called Think Like A Maths Genius, written by Arthur Benjamin and Michael Shermer. Some of the tricks are damn obvious, but I'll type it here anyway.

Chapter 0
Quick Tricks:
Easy (and impressive) Calculation

Instant Multiplication of 11

71 x 11
To solve this,, add the digits 7 + 1 = 8 in the middle of 7 and 1
71 x 11 = 781

How about
76 x 11
Similar way, 7 + 6 = 13
BUT the answer is not 7136
It should be done this way


1
736+
836

How about 3 digit numbers?
Simple. It can be done in similar way.
Eg. 123 x 11
1 + 2 = 3
2 + 3 = 5
123 x 11 = 1353

Multipying 2 2-digit number with the same first digit and second digit that sums to 10.

71 x 79
The first 2 digit will be 7 x 8 = 56
and The last 2 digit will be 1 x 9 = 9
so the answer is 5609.

*more will be added soon.