# Solving Project Euler Problem 42 – Coded Triangle Numbers

Following up from my previous post, where I attempted Solving Project Euler Problem 13 – Large Sum, I took up Problem 42 – Coded Triangle Numbers

While the original problem is a bit more complex, Hackerrank had broken it down a bit more simpler.

**Note**: This solution times out after the first 2 test cases out of a total of 7 test cases. So, while the solution is technically correct, it’s not the most optimal way to go about it.

#### Problem Statement

The nth term of a sequence of triangle numbers is given by,

tn= 0.5 n (n+1)

So the first ten triangle numbers are:

1,3,6,10,15,21,28,36,45,55,⋯

You are given an integer. If it is a triangular number tn, print the term n corresponding to this number, else print −1

#### Input Format

First line of input contains an integer T denoting the number of test cases. Each of the next T lines contains an integer.

#### Output Format

Print the answer corresponding to each test case in a new line.

#### Constraints

1≤T≤10^5

1≤tn≤10^18

#### Sample Input #00:

3

2

3

55

#### Sample Output #00:

-1

2

10

#### A Rough Solution:

```
def find_triangle_term(number)
flag = 0
(1..number).each do |num|
if number == (0.5 * num * (num + 1)).to_i
flag = num
else
flag = 0
end
break if flag > 0
end
(flag == 0)? -1:flag
end
test_cases = STDIN.readline().chomp.to_i
loop do
triangle_number = STDIN.readline().to_i
puts "#{find_triangle_term(triangle_number)}"
test_cases = test_cases - 1
break if test_cases == 0
end
```

#### Breakdown of the solution:

- Read the number of test cases from STDIN as an integer
- Loop over the test cases
- Read the set of numbers (1 on each line, 1 for each test case)
- Checking each input with the find_triangle_number() function and print the output
- find_triangle_num() function:
- Set a flag value
- Loop from 1 to the entered number, checking if it's a triangle number or not.
- Assign the term value to
`flag`

if it’s a triangle number - Assign 0 to
`flag`

if it’s not a triangle number

- Assign the term value to
- Check
`flag`

value and return`-1`

or the`flag`

value as appropriate

- find_triangle_num() function:

That's it, folks! I’ll be writing more about other problems I solve as and when they happen 🙂

Note: Solution files for this and any future Project Euler problems that I solve can be found here: Github: glnarayanan/ProjectEuler