If n is odd, multiply n by three then add one. If n is even, divide n by 2. Take that answer and repeat the process such that you have a sequence. For any positive even integer n, does the sequence ever not terminate at 1?

My thoughts:

- Any sequence which reaches 1 terminates as it enters the loop 1>4>2>1
- Any sequence which contains a number known to terminate at 1, also terminates at one
- All odd numbers do not need to be checked
- Take a and b to both be positive odd integers.
- a can be written as 2c+1 by the definition of an odd number
- b can be written as 2d+1 by the definition of an odd number
- a*b = (2c+1)(2d+1) by subsitution
- (2c+1)(2d+1) = 4cd+2c+2d+1 by distribution
- 4cd+2c+2d+1 = (4cd+2c+2d)+1 by association
- (4cd+2c+2d)+1 = 2(2cd+c+d)+1 by distribution
- 2(2cd+c+d)+1 is an odd number by definition. any integer multiplied by 2 and added to 1 is odd.
- Any odd number plus one is even by definition
- Therefore, after one iteration any odd number will become even.

- For any integer a where n is equal to 2^a the sequence will terminate at 1
- Since 2^a is even, and can be divided by 2 exactly a times, the product of each iteration becomes 2^a-k where k is the current iteration
- When a=k then the product of the iteration will be 2^a-a which is 2^0 which is equal to 1

- Any sequence which enters a loop of any size is considered terminated.
- Any sequence which diverges, or never repeats a number, is considered to grow to infinity

Based on the proof above, does that mean that a solution to the problem would be to determine if all the series eventually reach a point of 2^n? Thereby making the conjecture:

If n is even divide n by 2. If n is odd, multiply n by three and add one, then divide by two. Take that answer and repeat the process such that you have a sequence. For any positive integer n, does the sequence ever not contain a value 2^n?

]]>I will give you a coding puzzle to start. Whoever solves it with the most optimized solution will then write another puzzle. Puzzle 1:

How would you write randInt(A,B→C without using randInt(?

]]>-You could post a question about goto's

-You can post a bit of code that uses goto's that you would like to be fixed so that it does not use goto's

-You can post a bit of code likewise the above post except more of a contest for who can fix it/optimize it the best!

I'm interested in the last option the most. Teaching any programmer how to use loops to replace Goto's is very useful and skill-building for TI-Basic programming, in my opinion!

One question though: is there a way to post a puzzle into a forums, and then below have a sort of "Click to reveal solution" thing to put the solution in yet not give the answer away to everyone unless they want to see it? like what they have here (scroll down a bit)

So yeah. I might post a challenge later today

]]>"But I thought that only people without sin could cast the first…"

Oh, shut up, codebender! Post a riddle!

"OK, OK! Just don't hurt me!"

]]>What is the pattern in this series?

P.S. I do not know. Need creativity ]]>

You're in a game show, and there are 3 doors to pick from.

One has a car behind it, and the other two just have lumps of coal.

You get whatever is behind the door you pick, and you want a car!

You pick one.

To make the show more suspenseful, the host opens a door (that you didn't pick)

and you see that there is a lump of coal behind it. He then gives you the opportunity to switch.

What do you do?

**Bolded** text is example.

Image having 50 people in a house, they all wear a white or a black hat. They are not allowed to have any kind of conversation(no talking, pointing, whatever) and they are not allowed to touch each other (no pushing, pulling, …).

We want them to get out of the house and we want black and white hats seperated. How are we going to do this?

While exploring the Amazon rainforest, Professor VanderSommen was seized by hostile natives. These natives told the professor that they were going to kill him unless he could solve his way out of the following problem.

The professor had a choice of how they would kill him. Here's how it worked: The professor had to say something. It could be and sentence that wasn't a question. If the professor made a *false* statement, he would be hit with a wet noodle until dead. If he made a *true* statement, he would be forced to drink prune juice until dead.

What is the only statement that Professor VanderSommen can make which will save his life?

Have fun!

-Ace

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