An Intelligence test

 
 How is this possible ?


The sum of the numbers form the last  two digits and the difference between the numbers form the first digit.

Peculiar Numbers

The 3 digit numbers 407 and 370 have this peculiarity, that they exactly equal the sum of the cubes of their digits. Thus the cube of 4 is 64, the cube of 0 is 0, and the cube of7 is 343. Add together 64, 0, and 343, and you get 407. Again, the cube of 3 (27), added to the cube of 7 (343), is 370. Can you find a number not containing a zero that will work in the same way?

Solution: 

The other Numbers are 153 , 371.

   153 = 1 ^ 3 + 5 ^ 3 + 3 ^ 3 = 1 + 125 + 27 =  153

   371 = 3 ^ 3 + 7 ^ 3 + 1 ^ 3 = 27 + 343 + 1 = 371


Other numbers whose cube value are also same as the original number are 0 and 1.

    0   = 0 ^ 3 = 0

    1   = 1 ^ 3 = 1
   

Friends, If you could find any other such numbers...kindly let me know.


Thanks,

Multiplication Puzzle

Here is a simple multiplication puzzle.  It is not difficult, if properly attacked: 

A x B = B, B x C = AC, C x D = BC, D x E = CH, E x F = DK, F x H = CJ, H x J = KJ, J x K = E, K x L = L, 
A x L = L. 

Every letter represents a different digit form 0 to 9, and, of course, AC, BC, etc., are two-figure numbers. Can you find the values in figures of all the letters?


Friends, I have tried a solution for this puzzle. Don't have any idea if it's the correct solution. If you could find any other solutions, kindly let me know.

Thank you, 


A x B = B       1 x 3 = 3 
B x C = AC     3 x 5 = 15
C x D = BC     5 x 7 = 35
D x E = CH    7 x 8 = 56
E x F = DK    8 x 9 = 72
F x H = CJ    9 x 6 = 54
H x J = KJ    6 x 4 = 24
J x K = E       4 x 2 = 8
K x L = L        2 x 0 = 0
A x L = L        1 x 0 = 0 


So, the value of each letter is, 

A = 1
B = 3
C = 5
D = 7
E = 8
F = 9
H = 6
J = 4
K = 2
L = 0

Amazing Prime Numbers

Even if any number is deleted from these prime numbers,  these numbers will still remain prime.

23, 37, 53,73,113,131,137,173,179, 197, 311, 317,431, 617,719, 1499, 1997, 2239, 2293, 3137, 4919, 6173, 7433, 9677, 19973, 23833, 26833, 47933 ......




Examples:

23  -   If 2 is deleted, 3 is a prime, If 3 is deleted 2 is a prime.
137 - If 1 is deleted, 37  is prime, if 3 is deleted, 17 is prime, if 7 is deleted 13 is also a prime number.

An amazing fact !!

Pick a number between 1 and 99, and write it as a word.

Then count the letters.

Write the number of letters you counted in the word.

Repeat this process.

Within five times, you will end up at the number 4 every time. Just check it !!!



For Example,

Number 85 - Eighty Five

Number of letters - 10 Ten

Number of letters - 3 Three

Number of letters - 5 Five

Number of letters - 4 Four

Number of letters - 4 Four

.........

Amazing !!!!   
   

Cyclic Number

A  cyclic number is a number with "n" digits, when multiplied by the numbers 1,2,3,.......n, the result will be the same digits of that number but in different order.


Formula :

(bp-1 - 1) / p     Example:    Number = 142857,    142857 × 1 = 142857 142857 × 2 = 285714 142857 × 3 = 428571 142857 × 4 = 571428 142857 × 5 = 714285 142857 × 6 = 857142          Thanks, easycalculation.com

Basic Algebra Properties

Closure Axiom of Addition

Sum (or difference) of 2 reals equals a real number

Additive Identity

a + 0 = a

Additive Inverse

a + (-a) = 0

Associative of Addition

(a + b) + c = a + (b + c)

Commutative of Addition

a + b = b + a

Definition of Subtraction

a - b = a + (-b)

Closure Axiom of Multiplication

Product (or quotient if denominator 0) of 2 reals equals a real number

Multiplicative Identity

a * 1 = a

Multiplicative Inverse

a * (1/a) = 1     (a 0)

(Multiplication times 0)

a * 0 = 0

Associative of Multiplication

(a * b) * c = a * (b * c)

Commutative of Multiplication

a * b = b * a

Distributive Law

a(b + c) = ab + ac

Definition of Division

a / b = a(1/b)

Thanks, http://www.pleacher.com

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