# Probability (classical problem) and the experience of solving problems

Source: Internet
Author: User

Original question:

Description

Sometimes some mathematical results is hard to believe. One of the common problems is the birthday paradox. Suppose you is in a party where there is people including you. What's the probability that at least and the party has same birthday? Surprisingly the result is more than 0.5. Now this is the opposite. You are given the number of days in a year. Remember that's you can are in a different planet, for example, in Mars, and a year are 669 days long. You has to find the minimum number of people you has to invite in a party such that the probability of at least B peop The Le in the party has same birthday is at least 0.5.

Input

Input starts with an integer T (≤20000), denoting the number of test cases.

Each case contains an integer n (1≤n≤105) in a single line, denoting the number of days in a year in the plan Et.

Output

For each case, print the case number and the desired result.

Sample Input

2

365

669

Sample Output

Case 1:22

Case 2:30

Analysis:

Very bare computational probability problem, directly according to the test instructions simulation process is good.

Code:

#include <stdio.h>#include<string.h>#include<iostream>using namespacestd;intMain () {Doubleans; intT,n,kase=0; CIN>>T;  while(t--) {ans=1.0; Kase++; CIN>>N;  for(inti =0; I <= N; i++) {ans= ans* ((n-i)/(Double) n); if(Ans <=0.5) {printf ("Case %d:%d\n", Kase, i);  Break; }        }    }    return 0;}

Probability (classical problem) and the experience of solving problems

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