Interesting Facts ----> 41 - Speciality of 1681

Let's look at the number 1681

- It is 41 * 41 (just  coincidence that my Blog series is also 41 :))
- Now split 1681 into two parts - 16 and 81
- 16 is 4 * 4 and 81 is 9 * 9
- Drilling down further... 4 is again 2 * 2 and 9 is 3 * 3

Net-Net this is how it looks

Row 1 ---  1681
Row 2 ---    4  9   (Square root of 16 and 81)
Row 3 ---    2  3   (Square root of 4 and 9)

Now look further....

Look at the number in the second row - 49.

Square of 49 is 2401. Again if you subtract the digits 24 and 01 you get 23 which is the 3rd row in the above series :)

Can you find a number exhibiting similar pattern?

Please don't count numbers which end in "00" (like 3600, 8100)

Interesting Facts ----> 40 - Multiplication of two digit squares

This is an interesting way to find squares of two digit numbers - Need to test it for all combinations though but works for quite a few of them so far whatever I have tested :)

57
57
---
2549 (5*5 = 25, 7*7 = 49)
  70    (5+5) * 7 or (7+7) * 5 ----> Note the way 70 is written below the first line
-----
3249
-----

68
68
----
3684
  96
-----
4624
-----

46
46
----
1636
  48
------
2116
------

97
97
-----
8149
126 -------------> Notice how 126 is written due to the extra digit
-----
9409
-----

Interesting Facts ---> 39 - Check this sequence

Notice the following sequence -

Multiplication of successive primes results in a number which has a prime number again. Is this some sort of pattern or am I reading too much into it?


19 * 17 = 323 (23 is a prime number)

23 * 19 = 437 (37 is a prime number)

29 * 23 = 667 (67 is prime)

31 * 29 = 899 (89 is prime)

37 * 31 = 1147 ( 11 and 47 are primes)

41 * 37 = 1517 ( 17 is a prime)

43 * 41 = 1763 (17is a prime)

Interesting fact ---> 38 - Question for the day

Find the four digit number or number(s) satisfying this criteria

- The number is a perfect square - WXYZ
- If the Square root of the number is AB, then (A*A) + B = WX and (B*B) = YZ

Please note that there could be more than one correct answer for the above condition

Interesting fact ---> 37 - Multiples of 7

Check the scenarios below

7 * 6 = 42

Now reverse of 42 is 24 which is 7 * 3 + 3 (see how 6 is split as 3 + 3)

7 * 7 = 49

Reverse of 49 is 94 which is 7 * 13 + 3 (here 7 is split as 1 + 3 + 3 as in 13 and 3)

Can we find more patterns in this manner?

Interesting fact ---> 36 - Ramanujam Number and Anagram

Back to my favourite number again!

1729 = 12 ^ 3 + 1

Now look at one of the anagrams of 1729 ---> 9271

9271 = 21 ^ 3 + 10

21 is reverse of 12 and 10 is reverse of 1!

Ramanujam's number never ceases to amaze us even after so many years!!!  Wonderful discovery by a Great person...

Interesting fact ---> 35 - What is common among these numbers?

Can you find what is common between these four squares

2025, 3136, 6561, 8281

Interesting fact ---> 34 - What is unique about this square series?

What is unique and common about all the perfect squares between 1600 to 3600 and 8100 to 10000?

Interesting fact ---> 33 - Find this number

1. Its a 3 digit number - ABC

2. Add a digit (X) in the beginning and the resultant number is a perfect square - XABC

3. Add X to ABC and you get a perfect square - ABC + X

4. Add X as the second digit and the resultant number is still a perfect square - AXBC

5. Add Y as the 2nd or 3rd digit and still its a perfect square - AYBC, ABYC!

6. ABC itself has a special characteristic!

Find ABC

Interesting fact ---> 32 - Find these numbers

Find these 4 digit numbers which satisfy the following criteria

1. Its a perfect square

2. Remove first digit and the resultant is a perfect square

3. Remove first 2 digits and still we have a perfect square!

Interesting fact ---> 31 - What's next in the series?

Should be relatively a simple one - What's next in the series - 12, 36, 80, 150, ?

Interesting fact ---> 30 - Puzzle

Two Mathematicians are in a conversation and discuss about the development made on the technology front. They had numerous things to discuss and chose to refer to one of the path breaking development in the following way

- Two horizontal lines run in parallel and their left edges are supported by a straight line which extends beyond the second horizontal line
- Two slanting lines meet at one point and are connected in the middle through another line
- One of the earliest number cut into half
- Three horizontal lines run in parallel and their edges are connected by a vertical line
- A single digit numeral joined by a straight line
- This is followed by two circular balls which run one behind the other to meet two slanting lines converging at the same point on a vertical line

What are we talking about?

Interesting fact ---> 29 - Unique attribute among cubes

Back to cubes... 125, 216, 343, 512, 729 - One of the cubes has a special property compared to the others. Can you figure that out? Share any other attribute as well though one of them stands out for me

Interesting facts ---> 28 - Find this number

This should be relatively easier than the previous one (Puzzle 27)

Two boys discuss at length about a 4 digit number (ABCD)

Boy 1: The first two digits is a perfect square
Boy 2: Well...If you subtract AB-CD, then you get the square root of AB
Boy 1: That's a good one... But this is even better - If you interchange AB and CD and make it as CDAB, then its a perfect square
Boy 2: Excellent... But here's another beauty... If you add AB+CD it is the square root of CDAB!!!

Boy 1: That was a good one again - On top of this here's the clincher - The number ABCD is special in some way - It is the lowest number with.... (fill up the blanks)

What' the number?

Interesting facts ---> 27 - Question of the day

Two men start a conversation by looking at a 5 digit number

1st Man : Its a perfect square
2nd Man: If I remove 2nd digit, it is still a perfect square
1st Man: If I remove 1st 2 digits, it is still a square!
2nd Man: Sum of the digits is equal to the first 2 digits
1st Man: If you add first two digits with the last 3 digits (AB + CDE), the resulting number is difference of a perfect cube - perfect square
2nd Man: If I remove the 2nd and 4th digit, the resulting number is a perfect cube

What's the number?

Interesting fact ---> Question of the day

Question of the day - which number we are referring to here

1. Its a perfect square (3 digit number - XYZ)
2. It has 2 more anagrams which are perfect square
3. Insert a number as its second digit - And you get a perfect cube! (XAYZ)
4. Anagrams of XAYZ - Two of them again - They are also perfect square!

Interesting facts ---> 26 - Number in Focus - 3136

Some facts about the number 3136

1. Add 31 + 36 = 67, Subtract 36 - 31 = 5. Multiple 67 * 5 = 335. Now Add 3 + 3 = 6. Prefix 5 before that and you get 56 which is the Square root of 3136!

2. 3136 - Anagram is 3136 - Again one of the few numbers which has this pattern like 65536

3. Add 3+1 = 4. Add 3 + 6 = 9. Now add 4 + 9 = 13. Multiple 4 * 9 = 36. Now closely look at the original number 3136 - you will find 36 and 13 :)

4. Now take 56 which is the Square root of 3136. 56 + 5 + 6 = 67 which is sum of 31 + 36!

There are few more - Go ahead and add your comments!

Interesting facts ---> 25 - Number of the week! - 65536

After a week break due to busy schedule, back in action!

Let's look at the number 65536 - Very well known to the computer world :)

Some interesting facts about this number - few of them everyone is aware of and few more which are not so obvious

Encourage others to add to this since the primary intention of this series is to convey how we should look at numbers and patterns

1. The obvious one - Square root of 65536 is 256 which in turn is square of 16 which in turn is square of 4 and in turn square of 2

2. 65536 - One anagram of this is again 65536 - something which not many numbers can boast of

3. Now add the digits - You get 25 which is a perfect square! Now suffix 6 to 25 and you get 256 which is the square root of 65536 :)

4. Take the number 65536 and do this operation - (65 + 5) * 36 = 2520 which itself is a special number (Lowest number to have factors from 1 to 10)

5. In step 4 switch the operation - (65 * 5) + 36 = 361 which is a perfect square of 19

6. Now take the reverse of 65536 (63556) and repeat Step 5- (63 * 5) + 56 = 371 which is an Amrstrong number

The list goes on...

Interesting Number Pattern - 24 - Question!

Find this 4 digit number - call it as ABCD

- It is a perfect square
- If you reverse the number, it is also a perfect square (DCBA)
- The sum of the first two digits and the last two digits of the number is the square root of DCBA

Please don't use Google or don't write a  program :)

More than the answer just examine ABCD, DCBA after you are through and see how simple but beautiful the pattern is

Calculating the n-th root of a number - Question! - Interesting pattern - 23

How to calculate (217)^ 1/1025 -  217 to the power 1/1025

Well, everyone has a mobile or a PC which will do this but the intent is not to see how quickly a machine can calculate - rather what's the logic which we humans can use to do this calculation

I am opening this up as a question for others to share their view and then I will share some details as to how we can go about this

Clue: Start off with smaller numbers like 2nd, 3rd and 5th root :)

Sum of two consecutive Squares - Interesting Pattern ----> 22

Take a look at this patten

1 ^ 2 + 2 ^ 2 = 5
2 ^ 2 + 3 ^ 2 = 13
3 ^ 2 + 4 ^ 2 = 25
4 ^ 2 + 5 ^ 2 = 41
5 ^ 2 + 6 ^ 2 = 61 --------------------> Pattern breaks here
6 ^ 2 + 7 ^ 2 = 85
7 ^ 2 + 8 ^ 2 = 113
8 ^ 2 + 9 ^ 2 = 145
9 ^ 2 + 10 ^ 2 = 181
10 ^ 2 + 11 ^ 2 = 221 ------------------> Pattern breaks here

Continue this sequence - what do you notice?

Alternate results are either multiples of 5 or a Prime number except for situations when we encounter 5, 10, 15, 20.... (as the first number on the left) the pattern breaks for a brief while

Check this....

14 ^ 2 + 15 ^ 2 = 421
15 ^ 2 + 16 ^ 2 = 481 --------------> Pattern breaks here
16 ^ 2 + 17 ^ 2 = 545

Similarly...

19 ^ 2 + 20 ^ 2 = 761
20 ^ 2 + 21 ^ 2 = 841 --------------> Pattern breaks here
21 ^ 2 + 22 ^ 2 = 925

Squares ending with 5 - Interesting Number Pattern ---> 21

Notice this pattern for squares ending with 5

05 * 05 = 0025 ---> 00 + 25 = 25 ----> Subtract the original number 5  = 25 - 5 = 20
15 * 15 = 0225 ---> 02 + 25 = 27 ----> 27 - 15 = 12
25 * 25 = 625  ----> 06 + 25 = 31 ----> 31 - 25 = 6
35 * 35 = 1225 ----> 12 + 25 = 37 -----> 37 - 35 = 2

The sequence starts froom 20 and comes down to 2. Now notice this

45 * 45 = 2025 -----> 20 + 25 = 45 ------> 45 - 45 = 0
55 * 55 = 3025 -----> 30 + 25 = 55 ------> 55 - 55 = 0

So two zeroes in between as the difference... Now...

65 * 65 = 4225 -----> 42 + 25 = 67 ------> 67 - 65 = 2
75 * 75 = 5625 -----> 56 + 25 = 81 ------> 81 - 75 = 6
85 * 85 = 7225 -----> 72 + 25 = 97 ------> 97 - 85 = 12
95 * 95 = 9025 -----> 90 + 25 = 115 -----> 115 = 95 = 20

It shows the increasing pattern from 2 to 20 :)

Completes a full circle!

61 and 16 - Interesting Number Pattern ---> 20

These two numbers show some interesting pattern again

1. 61 * 61 = 3721. Difference between 37 - 21 = 16 which is the reverse of 61
2. Now reverse 37 which gives 73. Reverse 21 which results in 12. 73 - 12 = 61 :)
3. Sum of digits of 3721 ia 13.Sum of digits of 256 (16 * 16) is also 13!

Can you find some more?

51 and 153 - Interesting Number Pattern ----> 19

Can you find similar pattern exhibited by these two numbers

153 = 51 * 3

a) Notice that 5, 1, 3 form the digits 153

b) Reverse of 51 is 15 which is 1* 5 * 3

c) Now 15 * 15 = 225, 3* 3 = 9. 225 + 9 = 234

d) Now concatenate 234, 09 (3 * 3 again) - You get 23409 which is 153 * 153 :)

e) Top it all 153 is the Armstrong number which we all know of 153 = 1 ^ 3 + 5 ^ 3 + 3 ^ 3

Interesting Number Pattern ----> 18

Notice this pattern

13 * 13 = 169. Now sum up the digits as follows (01 + 69 = 70)

Reverse 13

31 * 31 = 961. Now sum up the digits again (09 + 61 = 70)

Now multiply 13 * 31 = 403. Sum up the digits again (04+03 = 07)

07 is the reverse of 70 :)

Try for 14

14 * 14 = 196 (01+96 = 97)

41 * 41 = 1681 (16 + 81 = 97)

14 * 41 = 574 (05 + 74 = 79)

79 is the reverse of 97 :)

There are more patterns and examples this way...

Interesting Number Pattern ---> 17

Look at the following pattern

51 ^ 2 = 2601 - Difference between 26 and 01 = 25 which is 5 * 5
61 ^ 2 = 3721 - Difference between 37 and 21 = 16 which is 4 * 4
71 ^ 2 = 5041 - Difference between 50 and 41 = 9 which is 3 * 3
81 ^ 2 = 6561 - Difference between 65 and 61 = 4 which is 2 * 2
91 ^ 2 = 8281 - Difference between 82 and 81 = 1 which is 1 * 1

Can we find similar pattern? Any reason as to why other squares (11, 21, 31, 41) don't show this pattern or is it hidden?

504 & 2520 - Interesting Number Pattern ----> 16

504 and 2520 have a special mention in the number world and this can be found out if we just Google

But there is more to these numbers

504 is the smallest number which has factors from 1 to 9

2520 is the smallest number which has factors from 1 to 10

Now 504 = 2 ^ 9 - 2 ^ 3 (512 - 8). Notice the base - 2 which plays a prominent role in this calculation

Look at this - 2 ^ 9 + 2 ^ 3 = 520. Prefix the number 2 to 520 and you get 2520 :)

Question for Maths lovers - Interesting Number Pattern ----> 15

Can you list down multiple characteristics of the number 153? (without Googling please :))

It could be sum of squares, cubes, etc, etc - Can you list down all of them?

Sum of Squares and Prime - Interesting Number Pattern ---> 14

Look at this

4 ^ 2 + 1 ^ 2 = 17 ---> Prime
9 ^ 2 + 4 ^ 2 = 97 ---> Prime
16 ^ 2 + 9 ^ 2 = 337 ---> Prime
25 ^ 2 + 16 ^ 2 = 881 ----> Prime
(The pattern breaks here) 36 ^ 2 + 25 ^ 2 = 1921 ----> Not a Prime but it is = 17 * 113 which are both primes :)

Anagram-Mania!!! Interesting Number Pattern ---> 12

One of the commonly known pattern is the following

a) 13 * 13 = 169
b) Anagram of 169 is 196 which is 14 * 14
c) 961 is also an anagram which is 31 * 31 (and 31 is anagram of 13!!!)

What makes this pattern more unique is when you add number "2" to the above pattern

1. Prefix 2 in front of 169 ---> 2169.
2. Now 2169 is = 2197 - 28. 2197 is in turn 13* 13 * 13 and 28 = 3 ^ 3 + 1 ^ 3 !!! Again you could see 31 and 13 in that combination :)
3. Anagram of 2169 is 9216 which is 96 ^ 2!
4. 9261 is also an anagram which is 21 ^ 3!!! Now jumble the numbers in 21 ^ 3 and make it 31 ^ 2 and you will get 961 with 2 moved out:)

Very tough to see such a pattern! But as always numbers continue to surprise us!

5625 - Interesting Number Pattern ---> 11

5625 - 75 * 75

Add 56 + 25 = 81 - 9 * 9

5625 is one of the few numbers which two squares has a subset - 625 and 25

Square + Cube pattern - Interesting Number Pattern ---> 10

Look at these patterns

2 ^ 3 + 1 ^ 2 = 9 = 3 ^ 2 (Now 2 + 1 = 3) - 2 and 1 are the base numbers

3 ^ 3 + 3 ^ 2 = 36 = 6 ^ 2 (Now 3 + 3 = 6) - 3 is the base number

4 ^ 3 + 6 ^ 2 = 100 = 10 ^ 2 (Now 4 + 6 = 10) - 4 and 6 are the base numbers

10 ^ 2 + 5 ^ 3 = 225 = 15 ^ 2 (Now 10 + 5 = 15) - 10 and 15 are the base numbers

Can you find more numbers of this nature?

Dedicated to Team India - Interesting Number Pattern --> 9

1983 - Difference between 83 and 19 is 64 which is a perfect square
2011 - Difference between 20 and 11 is 9 which is again a perfect square
2011 - Add the digits. It gives 4 which is a perfect square again
49 - Over in which India won the WC and also the number of runs Man of the Tournament Yuvi gave yesterday - Again a perfect square
91 - Runs scored by Dhoni which is a difference of two perfect squares 10 ^ 2 - 3 ^ 2!
277 - Winning score - Is a sum of 196 + 81 which are perfect squares in turn! (14 ^ 2 + 9 ^ 2)

All in all - A perfect ending to the WC story! Chak De India :)

Interesting Number Pattern --> 8

Check out these two

Take 13 and 11 which are prime numbers

13 X 11 = 143

Now reverse them and multiply again - 31  * 11 - 341 which is the anagram of 143!

Take 13 and 17 which are prime numbers

13 X 17 = 221 (or 0221)

Reverse them and multiply

31 X 71 = 2201 which is and anagram of 0221 :)

Interesting Number Pattern --> 7

Take a look at this

84 ^ 2 = 7056. Take a look at the following digits - 84, 70, 56 ---> This is a sequence with a different of 14. Can we find similar squares?

Interesting Number Pattern --> 6

 This is straightforward from a mathematical perspective and I am sure many of you will say - Oh it is there in the formula but still want to post this since we may not have noticed the pattern

18 * 9 = 162, 19 * 8 = 152... The difference is 10. How do arrive at this - 9 - 8 = 1, 1st digit is 1 (in tenth place) for both numbers - 1 * 10 = 10

27 * 8 = 216, 28 * 7 = 196... The difference is 20. 8 - 7 - 1, 1st digit is 2 (tenth place) for both numbers - 2 * 10 = 20

You can extraploate and get this pattern for many numbers

Well it is straightforward from a formulae perspective. Effectively you are doing the following - (10a + b) * c - (10a + c) * b = 10a (b - c)

But in real life we do miss out some interesting pattern even though they sound simple after looking at the formulae :)

Interesting Number Pattern --> 5

3969 square root is 63. 99 and 36 are the digits forming 3969. 99-36 gives 63 which is the original square root! Can we find similar numbers which show this pattern?

Interesting Number Pattern --> 4

Very simple but that it the amazing power of Numbers

89 ^ 2 = 7921. Add the first and last two digits - You get 100 which is a perfect square

Now look at the square of  98 ^ 2

98 ^ 2 = 9604. Add the first and last two digits - You again get 100!

98 is the reverse of 89!

Interesting Number Pattern --> 3

Take a look at the number 343. It is 7 ^ 3
Now look at 343 pretty closely - (3 + 4) ^ 3 = 343 :)

Inserting two mathematical operators between the digits give the original number!

There are very few numbers which have this pattern

Interesting Number Pattern --> 2

See this sequence

99 x 99 - 8901
89 x 89 - 7921
79 x 79 - 6241
69 x 69 - 4761
59 x 59 - 3481
49 x 49 - 2401
39 x 39 - 1521
29 x 29 - 0841
19 x 19 - 0361
9 x 9 - 0081

Note the last 2 digits from top to bottom - They follow the same pattern and difference is the same :)

Interesting Number Pattern --> 1

Interesting Pattern ----> 1 - How many such numbers are there similar to 9216 whose anagrams exhibit a cube or square pattern. Try to avoid numbers with many Zeroes :)

2916 - 54 ^ 2
9216 - 96 ^ 2
9261 - 21 ^ 3

96 - 54 = 42 which is a 21 * 2 :)