Interesting pattern - 48 - The number 3249

Look at this number 3249

It is 57 * 57

Now split this into two parts - 32 and 49

32= 2 ^ 5 (5 is first digit in 57)
49 = 7 ^ 2( 7 is 2 + 5!!!)

Now 32 + 49 = 81 = 9 ^ 2 = (2 + 7) ^ 2

Just look at how each patterns get formed with the numbers 2, 5, 7

May sound simple but pretty interesting to note the combinations that comes through

Amazing Facts - 47 - Squares of numbers ending with 7 - Do you see a pattern?

After a slightly long break, here I am back with a number pattern!

49 = 7 * 7
289 = 17 * 17
729 = 27 * 27
1369 = 37 * 37
2209 = 47 * 47
3249 = 57 * 57


Do you see a pattern? If yes, can you highlight the same

Puzzle No. 46 - Number of the day!

Assume the number as ABCD

1. First 2 digits and last 2 digits are successive multiples
2. If you add first 2 digits with last 2 digits you get a three digit number which has a special attribute (what's special about this number)
3. If you reverse the 4 digit number (DCBA) and add DC + BA you get a perfect square
4. DC and BA are even multiples of two prime numbers

Question Number 45 - Find the perfect square

Find the 4 digit number
- Its a perfect square
- Remove the 2nd digit an it is still a perfect square
- Add 3 to the second digit and again you get a perfect square
- Replace the first 2 digits by one of its factor and you get a perfect square again1

Mathematics question - Number 44

A reasonably simple Mathematics question before the week-end passes by...
Two Men are walking down a park and notices a car with 4 digit registration number
1st guy remembers the first 2 digits and 2nd one takes up the last two digits
1st Guy: If I add the first digit of your number to my 2 digit number, I get a perfect square
2nd Guy: If I subtract the second digit of your number from my 2 digit number, I get a perfect square as well
1st Guy exclaims... If we add both our 2 digit numbers, it is also a perfect square!
2nd Guy's turn now... The entire 4 digit number is a perfect square as well!
What's the 4 digit number they are referring to?

Interesting Pattern - 43 - Square of three digit number with zero as the middle digit

I am sure this is something which most of you are aware but it is worth a re-cap given the simplicity

Square of numbers with Zero as the middle digit

Start with 100's

1.) 104 * 104 = 10816

How do we arrive at this without going through usual multiplication steps

1*1 = 1, 4* (1+1) = 08, 4*4 = 16

Append them together and you get  10816

Alternate way to get the answer (have explained why this is required for few other scenarios in 5 and 6)

1
  08
      16
--------
10816

2.) 107 * 107 = 11449

1*1 = 1, 7 * (1+1) = 14, 7*7 = 49

3.) 204 * 204

2*2 = 4, 4 *(2+2) = 16, 4*4 = 16

Answer = 41616

4.) 209 * 209

2*2 =4, 9*(2+2) = 36, 9 * 9 = 81

Answer - 43681

It becomes a bit tricky when the middle value exceeds 2 digits like in the examples below. But all that's required is to shift that by one place and add instead of concatenation

5) 906 * 906

9*9 = 81, 6*(9+9) = 108, 6*6 = 36

81
  108
        36
--------
820836

6) 809* 809

8*8 = 64, 9*(8+8) = 144, 9*9 = 81

64
  144
        81
---------
654481


Anyway, some patterns are meant to be broken somewhere but its all fun as far as Maths is concerned and especially Numbers :)

Interesting Multiplication pattern ----> 42

Check these out...

23 * 103 = 2369 ----> 23 * 3 = 69 (obvious since we have multiplied 23 with (100 + 3)

Now reverse of 2369 is 9632 ----> 96/3 =32

34 * 102 = 3468 ----> 34 * 2 = 68 (again expected)

Now reverse of 3468 is 8643 ----> 86/2 = 43!

How many such patterns you can find? And any reason for some of the numbers showing this pattern?