Tuesday, April 16, 2013

Interesting Numbers...



Problem 1:

1. Take any three-digit number where the first and last digits differ by 2 or more.
2. Reverse the digits, and subtract the smaller from the larger one.
3. Reverse the digits again
4. Add to result in 3 to result in 2

Solution: Always you will get the number “1089"


Problem 2:

1.Take a four digit number with all different digits
2.Sort the digits in descending order and call it A
3.Sort the digits in ascending order and call it B
4.Calculate A-B
5.Repeat the process and get the unique number

Solution: After few iterations u will get the magic number "6174"


Problem 3:

Take a number (call it NumberOne) and sum up all its factors. Call it NumberTwo. Sum up all the factors of NumberTwo. If it is equal to NumberOne then these two numbers are called amicable numbers. For ex: 220,284
Sum of factors of 220: 1+2+4+5+10+11+20+22+44+55+110 = 284
Sum of factors of 284: 1+2+4+71+142 = 220
Find out these kind of amicable pairs.

Solution:  http://oeis.org/A063990

Problem 4:

If the sum of the factors of a number is equal to that number then it is called a perfect number …for example 6 Is a perfect number because factors of 6 are 3, 2, 1 and 3+2+1 = 6. 28 is a perfect number because factors of 28 are 14, 7, 4, 2, 1 and 14+7+4+2+1 = 28.Find out the magic numbers less than 100000 ( FYI there is only one magic number between 100-1000 and only one magic number between 1000 – 10000 and no magic numbers between 10000-100000).

Some interesting facts:

1. If 2exp(n)-1 is prime, then 2exp(n-1)*(2exp(n)-1) is a perfect number
2. All perfect numbers are even and in the form 2exp(n-1)*(2exp(n)-1).
3. There are no odd perfect numbers. If you find one file a patent
4. Any odd perfect number must exceed 10exp(300) and must be divisible by a prime power exceeding 10exp(20)
5. Perfect numbers are infinite. If you can prove the finiteness file a patent

Solution: http://oeis.org/A000396

Problem 5:

Take a number (call it NumberOne) and reverse all its digits. Call it NumberTwo. If NumberTwo is divisible by NumberOne then they are reverse digit divisible numbers.
For ex: 721 reverse: 127. 721 is divisible by 127.
Find out this kind of unique numbers.

Solution: Please ping me at: Gopala.Krishna@outlook.com

Problem 6:

There are two persons A and B
A knows the product of two numbers
B know the sum of the same two numbers
The numbers are between 2- 99
They started talking to each other
4 sentences exchanged between them
Based on the conversation we need to find the numbers

The conversation is:
1st: A says to B that he don't know the two numbers
2nd: B replies that i know u don't know the two numbers
3rd: A then replies NOW i know the two numbers
4th: B then replies NOW I ALSO know the two numbers

Solution: Please ping me at: Gopala.Krishna@outlook.com

Problem 7:

If a number is a square of an integer, and also the difference between cubes of two consecutive integers, then the square root of this number can be expressed as a sum of squares of two consecutive integers. For e.g. 169 = 512 - 343, so 13 = 4 + 9.
Find this kind of unique numbers.

Solution:  Please ping me at: Gopala.Krishna@outlook.com

If you like to know some more interesting problems of this kind please visit http://oeis.org/ or ping me at: Gopala.Krishna@outlook.com

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