100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 = ?
Since you can notice that there are fifty pairs of n^2 - (n-1) ^2,
n^2 - (n-1)^2 = n + (n - 1)
Thus 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 can also be written as
100 + 99 + 98+ ... + 2 + 1 = (100 x 101)/2 = 5050
It can be easily calculated that the digits 0 to 9 can be arranged into 3628800 distinct ten-digit numbers.
But I also know how many of these numbers are prime.
Do you?
Zero
The sum of numbers from zero to nine is 45 and can be divisible by 3 and 9.
A number can be multiplied by multiple of nine
i.e 9 18 27 36 45 ...
and the resulting number consist of only one digit.
Can you identify the number ?
12345679
12345679 × 9 = 111111111 (only 1s)
12345679 × 18 = 222222222 (only 2s)
12345679 × 27 = 333333333 (only 3s)
12345679 × 36 = 444444444 (only 4s)
12345679 × 45 = 555555555 (only 5s)
I can prove why 1 = 2
* Lets say y = x
* Multiply through by x xy = x2
* Subtract y2 from each side xy - y2 = x2 - y2
* Factor each side y(x-y) = (x+y)(x-y)
* Divide both sides by (x-y) y = x+y
* Divide both sides by y y/y = x/y + y/y
* And so... 1 = x/y + 1
* Since x=y, x/y = 1 1 = 1 + 1
* And so... 1 = 2
How is this possible ?
Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not following basic mathematical rules
I drive at an average speed of 30 miles per hour to the railroad station each morning and just catch my train. On a particular morning there was a lot of traffic and at the halfway point I found I had averaged only 15 miles per hour. How fast must I drive for the rest of the way to catch my train?
The train is just about to leave the station and there is no way I will be able to catch it this time.
Baseball bat and ball cost $50. If the bat cost $49 more than the ball, what is the cost of each
bat $49.50, ball $0.50
Using eight eights and addition only, can you make 1000?
888 + 88 + 8 + 8 + 8 = 1000
Create a number using only the digits 4,4,3,3,2,2,1 and 1. So i can only be eight digits. You have to make sure the ones are separated by one digit, the twos are separated by two digits the threes are separated with three digits and the fours are separated by four digits
41312432
Take 9 from 6, 10 from 9, 50 from 40 and leave 6.
How Come ??
SIX - 9 (IX) = S
9 (IX) - 10 (X) = I
40 (XL) - 50 (L) = X
===>SIX
2+3=8,
3+7=27,
4+5=32,
5+8=60,
6+7=72,
7+8=??
Solve it?
98
2+3=2*[3+(2-1)]=8
3+7=3*[7+(3-1)]=27
4+5=4*[5+(4-1)]=32
5+8=5*[8+(5-1)]=60
6+7=6*[7+(6-1)]=72
therefore
7+8=7*[8+(7-1)]=98
x+y=x[y+(x-1)]=x^2+xy-x