Blog #64 - Dedicated to Viswanathan Anand, the Chess Grandmaster!

Blog # 64 dedicated to the evergreen GOD of Chess - Viswanathan Anand!

New planet named after him with the number 4538 and the number does seems to be pretty special!

4538 - Square (53) + 1729 (Maths Genius Ramanujam Number!)
4538 - Square (67) + Square (7)
4538 - Square (64) + Square (21) + Square (1)

Anand has been the "King of 64 squares" in the Chess world and truly the number above does reflect that as well

And coincidentally this is also my 64th Blog!

Blog #63 - Find this number

Back with another question around a 4 digit number (ABCD) - again the digits can repeat and not necessarily distinct

1. AB + CD results in a number which is part of an unique number series
2. This number satisfies the condition X ^ Y where X and Y are positive integers
3. This number is a product of two numbers C and D and in turn if we add C + D it again results in a number which is part of a special series
4. C and D can also be expressed as X1 ^ Y1 and X2 ^ Y2
4. DCBA (reverse of this number) + a perfect square results in another well known number!

Find ABCD

Blog #62 - Is there a pattern in this number sequence?

1024, 2401, 4096, 9604 - Do these numbers exhibit any pattern and if yes, is there any other sequence which shows similar behaviour?

Feel free to share your inputs

Blog Post #61 - Five digit Number fun

Sunday musings!

Find this five digit number - ABCDE (Digits can repeat and not necessarily distinct)

- It can be expressed as (a ^ b) x (c ^ b) where a, b, c are integers
- (b ^ a) x (b ^ c) is a special number in its own sense
- Remove the 2nd digit (B) and it is a perfect square
- Add 1 to B and swap with A - (BACDE) and it is still a perfect square!

Blog #60 - X ^ Y - Y ^ X - An observation

I was randomly thinking through some of the scenarios for the formulae (X ^ Y) - (Y ^ X) where one is odd and other is even. For eg. ( 4 ^ 7) - (7 ^ 4)

Surprisingly, most of the resultant answer is either prime or a number whose factors are predominantly prime numbers and odd as well

3 ^ 4 - 4 ^ 3= 17
2 ^ 7 - 7 ^ 2 = 79
2 ^ 9 - 9 ^ 2= 431
4 ^ 5 - 5 ^ 4 = 399 (19 x 7 x 3)

Is there any pattern others see? And any justification using a mathematical equation (I did try logarithms but don't think it helps)

Blog #59 - Find the 4 digit number

- It is a 4 digit number (call it as ABCD)
- (AB + CD) ^ 2 is one of it anagrams
- One of its three digit anagram is also a perfect square
- ABCD - 1 results in a number which has 11 as one of its factor
- ABCD + 1 results in a number which is prime
- ABCD + 9 ^ 2 is again a perfect square
- Last not but not the least this number itself is pretty unique and famous for a reason (Clue: Uniqueness in terms of its factors)

Blog Post #58 - Armstrong number and their patterns

The well known Armstrong numbers are 153, 370, 371, 407 (apart from 0 and 1). Here are few more patterns exhibited by these numbers around squares, cubes and prime numbers

While most of the natural numbers will exhibit pattern of these sorts, it is interesting to see how fe number pairs play a larger role for these 4 numbers

a)  153

12 ^ 2 + 3 ^ 2
13 ^ 2 - 4 ^ 2

One of the anagram of 153 is 513 is 8 ^ 3 + 1 ^ 3

b) 370

7 ^ 3 + 3 ^ 3

19 ^ 2+ 3 ^ 2

One of the anagrams of 370 is 703 (which is not an Armstrong number but check the pattern)

703 = 19 x 37 (19 is there in earlier pattern exhibited by 370 and 37 is a subset of 370!)

c) 371

7 ^ 3 + 3 ^ 3 + 1 ^ 3 (sub of 3 different cubes)

One of the anagram of 371 is 731 which is formed by the digits 7, 3, 1 again

d) 407

7 ^ 3 + 4 ^ 3 or 7 ^ 3 + 8 ^ 2

Its anagram 704 is 7 ^ 3 + 19 ^ 2 (again notice the role number 19 plays in some of these numbers)

Last but not the least the Armstrong numbers show intricate relationship pattern among themselves

407 in turn is 370 + 37 (effectively 37 * 10, 37 * 11)
407 is also 371 + 6 ^ 2