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If you need any help in Physics or Mathematics (Page 2)

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akhl

IF-Rockerz

akhl

Joined: 30 March 2007

Posts: 5224

Posted: 11 September 2008 at 2:46am | IP Logged
Problem: There are 12 steps. I descend one step at a time or two at a time. In how many different ways can I come downstairs?
 
Solution:
Let f(n) = no of ways in which n steps can be descended.
One step can be descended in only one way - descend that step.
Therefore, f(1) = 1
 
Two steps can be descended in two ways - one way is to descend one step at a time and another way is to descend both steps at once.
Therefore, f(2) = 2
 
If you have to descend n steps, then you can choose any of the following two options
1. Descend one step. After that you have to descend n - 1 steps.
2. Descend two steps at once. After that you have to descend n - 2 steps.
Therefore, no. of ways to descend n steps = no. of ways  to descend n - 1 steps + no. of ways to descend n - 2 steps.
 
Or,
f(n) = f(n - 1) + f(n-2)
If we write the sequence of the values of f(n), then we get a sequence in which first term = 1 because f(1) = 1, second term = 2 because f(2) = 2 and after that each term is the sum of previous 2 terms. (Note: In case you are interested, it is Fibonacci sequence .)
 
There are 12 steps. Therefore, write the sequence for 12 terms.
f(1) = 1
f(2) = 2
f(3) = f(1) + f(2) = 1+2 = 3
f(4) = f(2)+f(3) = 2+3 = 5
f(5) = f(3)+f(4) = 3+5 = 8
f(6) = f(4) + f(5) = 5+8 = 13
f(7) = f(5) + f(6) = 8+13 = 21
f(8) = f(6) + f(7) = 13 + 21 = 34
f(9) = f(7) + f(8) = 21+34 = 55
f(10) = f(8) + f(9) = 34+55 = 89
f(11) = f(9) + f(10) = 55+89 = 144
f(12) = f(10) + f(11) = 89 + 144 = 233
 
No. of ways to descend 12 steps = f(12) = 233
 
Ans: 233
 

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laney

IF-Dazzler

laney

Joined: 14 September 2005

Posts: 3252

Posted: 11 September 2008 at 1:14pm | IP Logged
wow thanks for the answer but I dont really understand it, I think I have to talk to my teacher!
thanks anyways! Smile

akhl

IF-Rockerz

akhl

Joined: 30 March 2007

Posts: 5224

Posted: 11 September 2008 at 10:24pm | IP Logged
Let me know which part you did not understand and I will explain.

-Mystery-

IF-Veteran Member

-Mystery-

BollyCurry Buzzers

Joined: 31 August 2007

Posts: 20130

Posted: 12 September 2008 at 8:05am | IP Logged
Physics is stuff especially if it's calculus based.  I have taken the non calculus based physics in High school and didn't exactly love it but I'll be taking the Calculus based physics next year and let's see how that goes.

-Mahi

coolsonu

IF-Rockerz

coolsonu

Joined: 28 December 2005

Posts: 6645

Posted: 12 September 2008 at 10:12am | IP Logged
Originally posted by rajeev_fan

i hate physics. I dont understand a word of it...i think its coz of the teacher who teachs us...i dont understand even a single wrd of him....



it's the opposite for me!!!Embarrassed
I quite like Physics.. our teacher is awesome... we enjoy a lot in his period... he makes the all-boring topics interesting to study..Tongue we ask him sooooooo many questions...half of them r irrelevant and pretty stupid..yet he answers them with patience!!LOLBig smile We have a Physics class everyday..and i actually wait for it...
2 yrs back, i hated Physics like anything.. I think a lot depends on the type of teacher u have..

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