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:

Try another example

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

Showing 1 comment:

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.

12 days ago  Like

Next similar examples:

1. Perctentages
   35% of what number is 35?
2. What is 3
   What is the least common denominator of 11/15 and 12/19?
3. Boats
   Three-quarters of boats are white, 1/7 are blue and 9 are red. How many boats do we have?
4. Rectangle diagonal
   The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm².
5. Combinations 7
   A multi-course meal has 3 choices. 3 appetizers, 4 main courses, and 3 desserts. How many different combinations to choose from?
6. A report
   Maricris can type a committee report in 5 hours. Jane helped Maricris and together they finished the report in 3 hours. How long would it take Jane to complete the report she had worked alone?
7. Find sales tax
   What is 8.25% sales tax out of 1607.00?
8. The factory
   The factory z can complete an order in 12 days, factory p in 18 days. For how many days does an order completed when the first two days work only the factory z and then both factories?
9. Selling price
   Find the selling price. Cost to store: $50 Markup: 10%
10. Harvesters
    The first harvester will harvest the grain from the field in 20 hours, the second, the more powerful in 10 hours. How long will take harvest this field by both harvesters, if the second harvester has to be set up first and this takes 2 hours? The first har
11. Bob traveled
    Bob traveled 20 meters to Dave's house. He arrived in 3 minutes. What was his average speed for the trip.
12. RT - inscribed circle
    In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
13. On the 4
    On the way to playing disc golf with his two boys, Mr. Smith purchases 3 muffins and 2 bottles of water, totaling $9.75. The following week he only has Asher with him, so he purchases 2 muffins and 1 bottle of water totalling $6.00. What is the cost of on
14. Midpoint 4
    If the midpoint of a segment is (6,3) and the other end point is (8,-4) what are thw coordinate of the other end?
15. Coordinates of midpoint
    If the midpoint of the segment is (6,3) and the other end is (8,4) what are the coordinate of the other end?
16. Dirty road
    Mr. Smith is on a road trip to a remote disc golf course 180km away. He travels part of the way at 100km/h along the highway, and part of the way at 50km/h along dirt roads. If it took 2 hours to get there, how many hours did he spend on dirt roads?
17. Ladder
    Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder?