Odd/even number

Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by 3 and add 1. Now repeat the process with your new number. If you keep going, you'll eventually end up at 1. Every time. Prove. ..

Result

x =  1

Solution:

$n=12 \ \\ \ \\ n_{1}=12/2=6 \ \\ n_{2}=6/2=3 \ \\ n_{3}=3 \cdot \ 3+1=10 \ \\ n_{4}=10/2=5 \ \\ n_{5}=3 \cdot \ 5+1=16 \ \\ n_{6}=16/2=8 \ \\ n_{7}=8/2=4 \ \\ n_{8}=4/2=2 \ \\ n_{9}=2/2=1 \ \\ x=1$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Dr Math
always convergent to x = 1

see - https://en.wikipedia.org/wiki/Collatz_conjecture

he conjecture is named after Lothar Collatz, who introduced the idea in 1937, two years after receiving his doctorate. It is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.

Math student
it doesnt work

Next similar math problems:

1. Unknown number
Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The produ
2. Divisors
Find all divisors of number 493. How many are them?
3. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
4. Divisors
The sum of all divisors unknown odd number is 2112. Determine sum of all divisors of number which is twice of unknown numbers.
5. Numbers
Write smallest three-digit number, which in division 5 and 7 gives the rest 2.
In six baskets, the seller has fruit. In individual baskets, there are only apples or just pears with the following number of fruits: 5,6,12,14,23 and 29. "If I sell this basket," the salesman thinks, "then I will have just as many apples as a pear." Which
7. The dice
What is the probability of events that if we throw a dice is rolled less than 6?
8. Intelligence test
Paľo, Jano, Karol, and Rišo were doing an intelligence test. Palo correctly answered half of the questions plus 7 questions, Jano to a third plus 18 questions, Karol to a quarter plus 21 questions and Risho to a fifth plus 25 questions. After the test, K
9. Remainder
A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?
10. Red and white
Simona picked 63 tulips in the garden and tied bicolor bouquets for her girlfriends. The tulips were only red and white. She put as many tulips in each bouquet, three of which were always red. How much could Simon tear off white tulips? Write all the optio
11. Toy cars
Pavel has a collection of toy cars. He wanted to regroup them. But in the division of three, four, six, and eight, he was always one left. Only when he formed groups of seven, he divided everyone. How many toy cars have in the collection?
12. Nuts, girl and boys
Milena collected fallen nuts and called a bunch of boys let them share. She took a condition: the first boy takes one nut and tenth of the rest, the second takes 2 nuts and tenth new rest, the third takes 3 nuts and tenth new rest and so on. Thus managed
13. Sheep
Shepherd tending the sheep. Tourists asked him how much they have. The shepherd said, "there are fewer than 500. If I them lined up in 4-row 3 remain. If in 5-row 4 remain. If in 6-row 5 remain. But I can form 7-row." How many sheep have herdsman?
14. Hexagon = 8 parts
Divide the regular hexagon into eight equal parts.
15. Repair company
The company repairs cars. The first day repair half of the contract second day, the half of the rest and third day 8 residue cars. How many total cars company repaired?
16. Divisibility
Write all the integers x divisible by seven and eight at the same time for which the following applies: 100
17. Children
Less than 20 children is played various games on the yard. They can create a pairs, triso and quartets. How many children were in the yard when Annie came to them?