Understanding the 3x+1 Problem

The video introduces a mathematical problem involving a sequence of operations on numbers. Starting with any number, if it's odd, multiply by three and add one; if it's even, divide by two. The process is repeated, and the example given shows how numbers eventually fall into a loop of 4, 2, 1. The conjecture suggests that every positive integer will eventually reach this loop, known as the 4-2-1 loop.

What is the first step if the chosen number is odd?

• Subtract 1

• Multiply by 3 and add 1

• Multiply by 2

• Divide by 2

If a number is even, what operation should be performed according to the rules?

• Multiply by 3 and add 1

• Subtract 1

• Divide by 2

• Add 2

What sequence does the number 5 follow after applying the rules?

• 5, 16, 8, 4, 2, 1

• 5, 15, 45, 23, 11

• 5, 10, 20, 40, 80

• 5, 3, 9, 27, 81

What is the significance of the number 1 in the sequence?

• It is the starting point of the sequence

• It is the highest number in the sequence

• It is the lowest number in the loop

• It is the number where the sequence ends

What is the conjecture about the sequence of numbers?

• All numbers will increase indefinitely

• All numbers will eventually enter the 4-2-1 loop

• All numbers will eventually become zero

• All numbers will become negative