Mystery Number

Find the number that satisfies these two properties:

• The digits of add up to a number where equals times the number you get when you reverse the digits of .
• Reverse the digits of and find the prime factors of the number you get. Then take the sum of the squares of these prime factors and halve it. Removing the digit 0 from the new number yields back . 

Hint : is a four digit number.

http://plus.maths.org/content/mystery-number

Solution

The answer is 1729.  The number is known as the Hardy-Ramanujan number after Ramanujan and the mathematician and Godfrey Hardy. It has another interesting property: you can write it as a sum of cubes in two different ways:

Srinivasa Ramanujan, 1887-1920.

Hardy told the following story: "I remember once going to see [Ramanujan] when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. 'No,' he replied, 'it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.' "


http://plus.maths.org/content/mystery-number 

Mathematical Anagrams

An anagram is a word or phrase made up of the letters of another word.
These are all made up from maths words.

Friends, Kindly post the answers in the comment.

Source: Mathsphere math puzzles
 

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 !!!!