Collatz conjecture facts for kids
The Collatz conjecture is a conjecture (an idea which many people think is likely) in mathematics. It is named after Lothar Collatz. He first proposed it in 1937. It is about what happens when something is done repeatedly (over and over) starting at some number n:
- If n is even (divisible by two), n is halved (divide by two = take its half).
- If n is odd (not divisible by two), n is changed to .
The conjecture states that n will always reach one. Here is an example sequence:
- 28 (9 is odd, so we triple it and add one)
- 14 (28 is even; 14 is half of 28)
- 7 (14 is even, 7 is its half)
- 22 ()
- 16 (16 is a power of two, so it will lead to 1, halving each time)
- 1 (after 1 comes 4, 2, 1, 4, 2, 1, etc.)
Images for kids
Histogram of total stopping times for the numbers 1 to 100 million. Total stopping time is on the x axis, frequency on the y axis. Note that for all positive integers the histogram would be a completely different, exponentially-growing sequence (see #In reverse)
Collatz map fractal in a neighbourhood of the real line
Collatz conjecture Facts for Kids. Kiddle Encyclopedia.