[Guest]

Take any positive whole number not greater than 50. If the number is even, divide it by 2. if the number is odd, multiply it by 3 and add one to the result. Apply the same method to the resulting number, and continue in this way forming a chain of numbers until you finally arrive at the number 1. Shown below is the chain of numbers that results from this method if you begin with 15:

15->46->23->70->35->106->53->160->80->40>20>10->5->16->8->4->2->1

As you can see, the number 15 requires 17 steps to end up at the number 1.

Of the numbers less than 50, which takes the longest to reach the number one.

(Be patient as this riddle might take lots of time) Thanks and have fun!

[Guest]

might be easiest to work backwards?

[Guest]

Does that include the number 50?

Shouldn't this be in the new puzzles forum?

[Guest]

It will always have the same last 5 numbers:

16, 8, 4, 2, 1

Edited December 20, 2008 by yellowsubmarine

[Guest]

Worked this out:

50-25-76-38-19-29-88-44-22-11-34-17-52-26-13-40-20-10-5-16-8-4-2-1 (23)

49-148-74-37-112-56-28-14-7-22-11-34-17-52-26-13-40-20-10-5-16-8-4-2-1 (24)

So that means taking the numbers less than 50 out of the sequence we find out how many times it takes that number so here is my first list:

50:23

49:24

48:11

47:

46:

45:

44:16

43:

42:

41:

40:8

39:

38:20

37:21

36:

35:

34:13

33:

32:

31:

30:

29:18

28:

27:

26:10

25:22

24:10

23:

22:15

21:

20:7

19:19

18:

17:12

16:4

15:

14:17

13:9

12:9

11:14

10:6

9:

8:3

7:16

6:8

5:5

4:2

3:7

2:1

1:0

[Guest]

Could you please check my results to make sure they are correct

[Guest]

Worked this out:

50-25-76-38-19-29-88-44-22-11-34-17-52-26-13-40-20-10-5-16-8-4-2-1 (23)

49-148-74-37-112-56-28-14-7-22-11-34-17-52-26-13-40-20-10-5-16-8-4-2-1 (24)

So that means taking the numbers less than 50 out of the sequence we find out how many times it takes that number so here is my first list:

50:23

49:24

48:11

47:

46:16

45:

44:16

43:

42:

41:

40:8

39:

38:20

37:21

36:

35:13

34:13

33:

32:5

31:

30:

29:18

28:

27:

26:10

25:22

24:10

23:15

22:15

21:7

20:7

19:19

18:20

17:12

16:4

15:17

14:17

13:9

12:9

11:14

10:6

9:19

7:16

6:8

5:5

4:2

3:7

2:1

1:0

Edits in red

Edited December 20, 2008 by yellowsubmarine

[Guest]

50:23

49:24

48:11

47:

46:16

45:16

44:16

43:29

42:8

41:

40:8

39:33

38:20

37:21

36:21

35:13

34:13

33:25

32:5

31:

30:18

29:18

28:18

27:

26:10

25:22

24:10

23:15

22:15

21:7

20:7

19:19

18:20

17:12

16:4

15:17

14:17

13:9

12:9

11:14

10:6

9:19

7:16

6:8

5:5

4:2

3:7

2:1

1:0

Edits in red

27 is the longest, i got to 66 and gave up, 41 2nd, 31 3rd and 47 4th. I got this because all the numbers are in the 27 sequence.

[unreality]

The 3X+1 problem is interesting because it still hasn't been proven to always converge to 1 (if you start with a positive integer I mean)

edit: I'm sure wikipedia has an article on the subject

aaand yes they do: http://en.wikipedia.org/wiki/3x%2B1

Edited December 20, 2008 by unreality

[Guest]

I hacked together a Perl script to verify the results.

for (my $i=50; $i>=1; $i--) {

  my $ct=0, $j=$i, $chain=$j;

  while ($j>1) {

    $j = $j%2 ? $j*3+1 : $j/2;

    $chain .= "->$j";

    $ct++;

  }

  printf("%2d = %3d\n",$i,$ct,$chain);

}

[/codebox]

[spoiler=Perl script results]50 = 24

49 = 24

48 = 11

47 = 104

46 = 16

45 = 16

44 = 16

43 = 29

42 = 8

41 = 109

40 = 8

39 = 34

38 = 21

37 = 21

36 = 21

35 = 13

34 = 13

33 = 26

32 = 5

31 = 106

30 = 18

29 = 18

28 = 18

27 = 111

26 = 10

25 = 23

24 = 10

23 = 15

22 = 15

21 = 7

20 = 7

19 = 20

18 = 20

17 = 12

16 = 4

15 = 17

14 = 17

13 = 9

12 = 9

11 = 14

10 = 6

9 = 19

8 = 3

7 = 16

6 = 8

5 = 5

4 = 2

3 = 7

2 = 1

1 = 0

[/spoiler]

[spoiler='final list]50:23

[color=#000000]49:24

48:11

47:

46:16

45:[color=#FF0000]16[/color]

44:16

43:[color=#FF0000]29[/color]

42:[color=#FF0000]8[/color]

41:

40:8

39:[color=#FF0000]33[/color]

38:20

37:21

36:[color=#FF0000]21[/color]

35:13

34:13

33:[color=#FF0000]25[/color]

32:5

31:

30:[color=#FF0000]18[/color]

29:18

28:[color=#FF0000]18[/color]

27:

26:10

25:22

24:10

23:15

22:15

21:7

20:7

19:19

18:20

17:12

16:4

15:17

14:17

13:9

12:9

11:14

10:6

9:19

7:16

6:8

5:5

4:2

3:7

2:1

1:0[/color]

[/spoiler]

Edits in [color=#FF0000]red[/color]

[spoiler=guess]27 is the longest, i got to 66 and gave up, 41 2nd, 31 3rd and 47 4th. I got this because all the numbers are in the 27 sequence.[/spoiler]

[Guest]

Edits in red

27 is the longest, i got to 66 and gave up, 41 2nd, 31 3rd and 47 4th. I got this because all the numbers are in the 27 sequence.

50:23

49:24

48:11

47:

46:16

45:16

44:16

43:29

42:8

41:

40:8

39:33

38:20

37:21

36:21

35:13

34:13

33:25

32:5

31:

30:18

29:18

28:18

27:

26:10

25:22

24:10

23:15

22:15

21:7

20:7

19:19

18:20

17:12

16:4

15:17

14:17

13:9

12:9

11:14

10:6

9:19

7:16

6:8

5:5

4:2

3:7

2:1

1:0

Yup That's right it has 100 steps in it Yay!

[Guest]

I hacked together a Perl script to verify the results.

for (my $i=50; $i>=1; $i--) {

  my $ct=0, $j=$i, $chain=$j;

  while ($j>1) {

    $j = $j%2 ? $j*3+1 : $j/2;

    $chain .= "->$j";

    $ct++;

  }

  printf("%2d = %3d\n",$i,$ct,$chain);

}

[/codebox]

[spoiler=Perl script results]50 = 24

49 = 24

48 = 11

47 = 104

46 = 16

45 = 16

44 = 16

43 = 29

42 = 8

41 = 109

40 = 8

39 = 34

38 = 21

37 = 21

36 = 21

35 = 13

34 = 13

33 = 26

32 = 5

31 = 106

30 = 18

29 = 18

28 = 18

27 = 111

26 = 10

25 = 23

24 = 10

23 = 15

22 = 15

21 = 7

20 = 7

19 = 20

18 = 20

17 = 12

16 = 4

15 = 17

14 = 17

13 = 9

12 = 9

11 = 14

10 = 6

9 = 19

8 = 3

7 = 16

6 = 8

5 = 5

4 = 2

3 = 7

2 = 1

1 = 0

[/spoiler]

Did it go wrong somewhere because the answer is right but it has the wrong number of steps

[Guest]

43 with 29 steps.

[Guest]

43 with 29 steps.

Mo sorry the real answer has wayyyyy more steps.

[Guest]

Did it go wrong somewhere because the answer is right but it has the wrong number of steps

I got 111 steps too.

[Guest]

Did it go wrong somewhere because the answer is right but it has the wrong number of steps

These are the 111 steps from 27 down to 1. Looks all right to me.

27

->82->41->124->62->31->94->47->142->71->214

->107->322->161->484->242->121->364->182->91->274

->137->412->206->103->310->155->466->233->700->350

->175->526->263->790->395->1186->593->1780->890->445

->1336->668->334->167->502->251->754->377->1132->566

->283->850->425->1276->638->319->958->479->1438->719

->2158->1079->3238->1619->4858->2429->7288->3644->1822->911

->2734->1367->4102->2051->6154->3077->9232->4616->2308->1154

->577->1732->866->433->1300->650->325->976->488->244

->122->61->184->92->46->23->70->35->106->53

->160->80->40->20->10->5->16->8->4->2

->1

[Guest]

hmm I must have made a mistake somewhere... Good job for clarifying

Edited December 29, 2008 by Riddle Master Zack

[Guest]

Will this work for any number, or only numbers that are less than 50 that is positive?

Edited December 31, 2008 by Mystery

[Guest]

Will this work for any number, or only numbers that are less than 50 that is positive?

It should be any number, but it might take a wayyy longer time for some numbers.