The Simplest Math Problem No One Can Solve - Collatz Conjecture

If you have an odd number in the Collatz Conjecture sequence, what is the next step?

• Divide the number by 2.

• Multiply the number by 3 and add 1.

• Subtract 1 from the number.

• Multiply the number by 2.

What is the main idea of the Collatz Conjecture?

• All numbers eventually become prime numbers.

• All positive integers eventually reach the 4-2-1 loop when specific rules are applied.

• All even numbers are multiplied by three and one is added.

• All odd numbers are divided by two.

Why are the numbers generated by the 3x+1 rule called "Hailstone Numbers"?

• They are very cold, like hailstones.

• They are small and round, like hailstones.

• They go up and down in value, similar to hailstones moving in a thundercloud.

• They are hard to predict, like where hailstones will fall.

Benford's Law is a mathematical principle that can be used to detect what?

• The next number in a random sequence.

• Fraud in financial documents or election results.

• The highest point a number will reach in the Collatz Conjecture.

• The exact number of steps a sequence will take to reach one.

How does the 3x+1 rule behave when applied to negative numbers?

• It always leads to the number 1.

• It creates multiple independent loops.

• It never forms any loops.

• It always leads to negative infinity.

As you consider larger and larger numbers, what happens to the percentage of perfect squares among them?

• It increases.

• It stays the same.

• It decreases.

• It becomes exactly 10%.

Why is testing a very large number of cases not enough to prove a mathematical conjecture true for all numbers?

• Computers can make errors when checking many numbers.

• A counter-example might exist that is beyond the tested range.

• Mathematical conjectures can only be proven by experiments.

• Only small numbers follow mathematical conjectures.

What does it mean if a mathematical problem is "undecidable"?

• It means the problem is too difficult for humans to solve.

• It means the problem has no correct answer.

• It means it's impossible to prove whether the problem is true or false.

• It means the problem can only be solved by guessing.