## 22 September 2014

### Quiz 33: Find the index of first even element from a series

Problem:
For 1st row, element of a series is 1, for 2nd row, elements are 1,1,1. From 3rd row onwards, series increases by 1-1 elements at left and right of previous row such that each element is sum of 3 elements of above row(ie element immediately above and elements to left and right).
ie
1st row-                          1
2nd row-                    1   1   1
3rd row-                1   2   3   2   1
4th row-            1   3  6   7   6    3   1 (and so on)

Find the index of 1st element which is even for Nth row. Index starts with 1.

Input Format:
first line, T, contains number of test cases
T lines containing N

Output Format:
Index of first even element for N

Constraints:
N>2

Sample Input
4
3
4
8
98

Sample Output:
2
3
3
4

Explanations:
for 4, series is 1 3 6 7 6 3 1, so 6 is first even number and index is 3.

Solution:

@out=();
chomp(\$t=<STDIN>);
for(\$i=0;\$i<\$t;\$i++)
{
chomp(\$n=<STDIN>);
if(\$n%2 == 1)
{
push(@out,2);
next;
}
\$trd=\$n*(\$n-1);
\$trd=\$trd/2;
if(\$trd % 2 eq 0)
{
push(@out,3);
next;
}
push(@out,4);
}
foreach(@out)
{
print "\$_\n";
}

Tips:
If N is odd, answer is 2 always. 3rd elements is n(n-1)/2, check if this is even->answer is 3. Otherwise answer is 4 always.