You are given 100 cards numbered 100,98,99, ............, 3,2,1, in that order . You want to put them in the order 1,2,3, ............., 99,100 switching only two adjacent cards at a time. If the minimum number of switches necessary is n, then |n - 5000| is equal to. Please explain.
Answers
Answered by
0
Step-by-step explanation:
use the formula of n and get the answer
Answered by
4
Answer:
50
Step-by-step explanation:
You have to switch only adjacent cards, so take card no. 1 it has to be at the 100th position, so on 1st switch it comes at 2nd position, on 2nd switch it comes to 3rd position, and so on... If you notice for taking the card at 'p' position you need (p-1) switches, so for 100th position you need 99 switches. Likewisely for 2nd card 98 switches and so on... For 100th card 1 switch. So total switches would be= n(n+1)/2=> 99(99+1)/2 =4950 switches and n= 4950.
Therefore |n-5000| = |4950-5000| = 50 ( by using mod we neglect its sign and only consider the magnitude).
Therefore answer is 50.
Alternately you can solve it by nCr method
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