There are many complex math puzzles that have stumped mathematicians and puzzle enthusiasts alike. Here are 5 mathematical conjecture puzzles that I have attempted to explain and solve using Python:

**The Collatz Conjecture**

The Collatz conjecture is a mathematical problem that involves a sequence of positive integers that are generated according to a specific rule. The conjecture states that for any positive integer, the sequence will eventually reach the number 1, regardless of the starting number.

Here is a simple Python function that generates the Collatz sequence for a given starting number:

```
def collatz(n):
while n != 1:
print(n, end=", ")
if n % 2 == 0:
n = n // 2
else:
n = 3*n + 1
print(1)
```

To use this function, you would simply call it with a positive integer as the argument, like this:

```
collatz(10)
```

This would output the following sequence:

```
10, 5, 16, 8, 4, 2, 1
```

The conjecture has been verified for many starting numbers, but it has not been proven for all positive integers. Despite much effort, a general proof or counterexample has not yet been found.

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