Pattern Recognition - 44

Find the next two numbers in the series.

0, 3 , 8 , 15 , 24 , 35 , 48 ,_ ,_ , ...............


Answer


Tn=(n *n) -1

T1=(1 *1) -1 = 0


T2=(2*2) -1 =3

T3=(3 *3) -1=8


T4=(4 *4) -1=15

T5=(5 *5) -1=24


T6=(6 *6) -1=35

T7=(7 *7) -1=48


T8=(8 *8) -1=63

T9=(9 *9) -1=80


0, 3 , 8 , 15 , 24 , 35 , 48 , 63 , 80, ...............

Pattern Recognition - 43

Find the next two numbers in the series.

0 , 7 , 26 , 63 , 124 ,_ ,_ ..................

Answer

Tn=(n * n * n) -1

T1=(1 * 1 * 1) - 1 =0

T2=(2 * 2 * 2) -1 = 7

T3=(3 * 3 * 3) -1 =26

T4=(4 * 4 * 4) -1 = 63

T5=(5 * 5 * 5) - 1= 124

Next two numbers (6 * 6 * 6) -1 = 216 - 1 =215
                            (7 * 7 * 7) -1= 343-1 =342


0 , 7 , 26 , 63 , 124 , 215 ,342,.....................

Pattern Recognition - 42

Find the next two numbers in the series.

64 , 4 , 2 , 729 , 9 ,3 , 4096, 16 , 4 , 15625 , _ , _ ,..................



Answer


64 , 4 , 2 , 729 , 9 ,3 , 4096, 16 , 4 , 15625 , _ , _ ,..................

64 , 4 , 2     4= (2*2)   64=(4 * 4 *4)

729 , 9 ,3     9=(3*3)   729 =(9 * 9 * 9)

4096, 16 ,4 16=(4*4)   4096=(16 * 16 * 16)

63125         (15625 )^(1/3)= 25 Or 25 ^ 3=15625       
25=(5 * 5)

64 , 4 , 2 , 729 , 9 ,3 , 4096, 16 , 4 , 15625 ,  25 , 5 ,..................

Math IQ

Statement A : If (X * X)=(Y *Y) then X is always equal to Y.

Statement B: If (X * X * X)=(Y * Y * Y) then X may not be equal to Y.

1. A- true B-false     2. A-false  B- true      3. Both are true.     4. Both are false.




Source: Internet 

Answer

Statement A : (X * X)=(Y *Y)    X may not be always equal to Y because   (1*1)=(-1 * -1) here X # Y

Statement B: X is always equal to Y because if we take a minus number as in the above mentioned case
                         (1*1 *1) # (-1 * -1 * -1)

Both are false.

But if we consider imaginary numbers then statement B will be true. One guy in our company (from UK) gave an excellent answer.

"Statement B depends on whether we are using just integers or extending to include imaginary numbers. If it is just integers the statement is false but if we are using imaginary numbers then the statement is true since there are 3 cubed roots of -1. Y could therefore be -1 and X could be one of the other 2 roots e.g. 1/2 + i* (sqrt(3)/2)."

Pattern Recognition - 41

Find the next number in the series.

279, 358 , 437 , 516, _ ,.................

Answer


279, 358 , 437 , 516, _ ,.................

2 , 3 , 4 ,  5, 6,.........

7 , 5 , 3 ,  1, -1,.........

9 , 8  , 7 ,  6, 5,.........

So the answer is suppose to be  6 -1 5  Oops I did not realize there we go to minus range. There is really no answer if we consider this pattern. :)

But the same person who answered to the "Math IQ" has given an excellent answer to this too. :)


Maybe the answer could be:

 

( ( x + 1) x 100) + ( (9 - 2x) x 10 ) + (10 - x )

 

 

so for x = 1:

 

((2) x 100) + ( (9 - 2) x 10 ) + (9) = 279

 

x = 2:

 

((3) x 100) + ((9 - 4) x 10) + (8) = 358

 

x = 3:

 

((4) x 100) + ((9 - 6) x 10) + (7) = 437

 

x = 4

 

((5) x 100) + ((9 - 8) x 10 ) + (10 - 4) = 516

 

So then the next in the sequence would be:

 

x = 5

 

((6) x 100) + ((9 - 10) x 10) + (10 - 5) = 600 - 10 + 5 = 595

 

and so on.....

 

And the equation at the top can be rewritten more simply as:

 

79x + 200

 

and that will give the same result:

 

x = 1: 79 + 200 = 279

x = 2: 158 + 200 = 358

x = 3: 237 + 200 = 437

x = 4: 316 + 200 = 516

x = 5: 395 + 200 = 595

After I checked the above answer only I realized there is another pattern in the series.

27  9, 35  8 , 43  7 , 51  6, _ ,.................
27 , 35 , 43 , 51 , 59, .............................
    +8   +8   +8  +8
9,  8,  7  ,  6,  5,.......................
   -1  -1  -1   -1

Answer 59 5    595

Pattern Recognition- 40

 Find the next two numbers in the series.

1 ,2 , 6 , 15 , 31 , 56 ,_ , _ .......

Answer

1  ,  2 ,    6 ,   15 ,  31 ,  56 ,
    +1   +4  +9    +16   +25

1= 1 *1
4=2 * 2
9=3 * 3
16=4 * 4
25=5 * 5

Next two numbers  56 + (6*6)  = 92
                             92 + (7 *7)= 141

1, 2 , 6 , 15 , 31 ,56 , 92 , 141 ,........

Love you Linzie !

Linzie was sitting still; eyes filled with tears. Henry was a bit shocked and confused to see tears in her eyes where he rather had expected a delighted face.

What is wrong with Linzie? Let us go back in time.

   

It was a Friday night. Linzie and Henry just had their dinner. Henry, a smart and geeky software developer looking at his laptop seriously like if he is trying to figure out a way to send rocket to Mars. Linzie, a full time house wife that whole heartedly enjoys her job.After completed her cleaning work in the kitchen, Linzie comes and sit next to Henry.

 

Linzie : You still working dear? ! Do you remember it is Friday night?

Henry: Yeah, I have some work pending to be completed for the week. I had to lend hand to a friend from some other team during day time to resolve a critical issue in their project.

Linzie : That’s great. By the way I have a small question for you? !

Henry : Yes?  !

Linzie : Do you think I’m the right person for you?

Henry: Why this question all of a sudden?

Linzie : It’s been there for a while. But it came out today only.

Henry: Of course, you are the perfect match for me.

Linzie : You are a very high tech person. I don’t go much into the basics even. I wish I was able to help you with your work.

Henry : oh… Come on Lin! Do you know that you are the inspiration for me to do a good quality job? Actually you are the one who taught me all the basics that helped me to become a successful techie.

Linzie : I helped you? ! how? I do not get anything at all.

Henry: Let me explain

 

1. There is a concept called threading in software programming. Rather than waiting for one big time consuming process to complete, let it run in the background and let others work in parallel.The way you handle multiple jobs like answering a phone while making coffee helped me understand multitasking and I’m able to build efficient and responsive programs with it.
2. Some days you make excessive amount of food and keep them in refrigerator. So we do not to spend a lot of time every day for cooking. I use the very same theory in programming. I do not do expensive and time consuming data retrieval from database every time when I need it. Rather I store the retrieved data in a cache and use them till they become expired.
3. There is a concept called pre-compilation in SQL where prepare things beforehand and keep them ready for use. The days when you need to cook for me in the morning, you cut the vegetables and keep everything ready on the previous night itself. That helped me understand the theory very well and I use it in programming where ever possible and appropriate.
4. Every time once you done with cooking, you clean the vessels and put them back in place neatly so no one will feel uncomfortable coming to kitchen and do some preparation. That taught me the concept of refactoring.  Refactor the code once completed the implementation so the code will look more neat and readable.
5. When you place the ingredients in the kitchen cupboard you arrange them category wise so main ingredients are in one segment, spices are in another segment likewise which taught me to arrange my code region wise so the system events will be in one region, custom functions written by me will be in another region etc etc. Hence when I go and look at my code after a while or if someone else got to go through my code, anyone can locate the places easily.
6. One thing I appreciate is you have labeled all the ingredient bottles and boxes in the kitchen so I can easily identify the items just by looking at the label when you are not at home. I follow the same good practice in programming where I give meaningful names for variables and methods as much as possible.
7. Every week you take clothes out of suitcase and arrange them in the front part of dressing cupboard which helped me to understand the concept of keeping frequently accessed objects in memory so time and effort for the retrieval can be reduced.

And there are many more. Still do you think you are right?

 

(Flash back ends)

 

Linzie looked in to the worried eyes of henry wiping her own tears out.

“No. I’m perfectly alright.It’s tears of joy. I was overwhelmed by your response and your love even though I did not understand the programming part of those theories. I’m so lucky. Love you honey”

“Love you too Linzie!”

 

Henry’s mind voice: “Thank God. No more questions.  I can peacefully work.”