UVA - 11614 - Etruscan Warriors Never Play Chess

 #include <stdio.h>
#include <math.h>

int main()
{   int i,cases;
    long sum;
    scanf("%d",&cases);
    for(i=0;i<cases;i++){
        scanf("%ld",&sum);
        printf("%ld\n",(long)((-1+sqrt(1+8*sum))/2.0));
    }
    return 0;
}