What is Collatz conjecture?
Is Collatz conjecture always true?
What so special about 3x+1 ? ​

Step-by-step explanation:

The Collatz Conjecture is one of the most intreging of all the possible simple statements in mathematics.

Simply put it says

if a number is even, divide by 2If a number is odd, multiply by 3 and add1. or 3x + 1The result will always wind up in a loop. Neat huh!!! Where you wind up going over the same numbers over and over. You can't escape the loop.

Try 5

It's odd so triple it and add 1. You get 1616 is even. Divide by 2. You get 88 is even. Divide by 2. You get 44 is even. Divide by 2. You get 22 is even. Divide by 2. You get 11 is odd. Triple it and add 1. You get 4. You can see you wind up doing 4 2 1 forever. The Collatz conjecture has not been proved, but every number up to 2^68 has been shown to go to this loop eventually.

Try another one -- 15. On the 16th move it goes from 4 to 2 to 1 and then keeps on repeating those 3 digits.

Take 15It's odd. Triple it and add 1. That gives 46.46 is even. Divide by 223 which is odd. Triple it and add 1  = 7070 is even. Divide by 2. 3535 is odd. Triple and add 1.  106  which is even53 which is odd.  Triple it and add 1. You get 160160 is even. Divide by 2. You get 8080 is even Divide by 2. You get 4040 is even. Divide by 2. You get 2020 is even. Divide by 2. You get 1010 is even. Divide by 2. You get 55 is odd. Triple it and add 1. You get 1616 is even. Divide by 2. You get 88 is even. Divide by 2. You get 44 is even. Divide by 2.. You get 2.2 is even. Divide by 2. You get 11 is odd and you are in the loop because you get 4 which you have already done.

X= 2 he can buy 2 packs of cards for $12 and an action figure for $3 so he would spend $15 in total plus the free poster