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12-11-2004 02:14 PM  13 years agoPost 1
rchelipilot121

rrNovice

Crap!! I'm here again!!

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It's simple though. Let's see who gets it first.

Take any positive, whole number not greater than 50. If the number is even, divide it by two. If the number is odd, multiply it by 3, and add 1 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. Below is the chain of numbers that results from this method if you begin with 10....

10-5-16-8-4-2-1

As you can see, the number 10 requires 6 steps to end up at 1.

Of the numbers not greater than 50, which takes the most steps to reach the number 1?

BONUS-Can all whole numbers be traced back to one? Are you SURE?

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12-11-2004 02:36 PM  13 years agoPost 2
Ringding

rrApprentice

Austria

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Considering this is still an unresolved mathematical problem, do you expect runryder members to solve it?

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12-11-2004 02:39 PM  13 years agoPost 3
rchelipilot121

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The bonus MAY be unresolved, but I have faith if someone here works hard at it all day, they may come up with an answer.

However, the first question does have an answer. (that way no one gives up)

re-edited the riddle to make the questions distinct...

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12-11-2004 03:11 PM  13 years agoPost 4
Graeme

rrApprentice

Jeffersonville, IN, USA

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Part 1. 27: 111 steps

Part 2. I'm no mathemetician, but it would seem to me that the only whole number not based on 1 would be 0.



Give a man a program and you frustrate him for a day; teach him to program and you frustrate him for life.

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12-12-2004 06:28 AM  13 years agoPost 5
extremeflying

rrVeteran

Thailand

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let me try

30-15-46-23- oh i give up

Oh..shiiieeettt !!!

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12-12-2004 07:17 AM  13 years agoPost 6
noname

rrVeteran

Woodinville, WA

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1: 4, 2, 1, - 3
2: 1, - 1
3: 10, 5, 16, 8, 4, 2, 1, - 7
4: 2, 1, - 2
5: 16, 8, 4, 2, 1, - 5
6: 3, 10, 5, 16, 8, 4, 2, 1, - 8
7: 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 16
8: 4, 2, 1, - 3
9: 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 19
10: 5, 16, 8, 4, 2, 1, - 6
11: 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 14
12: 6, 3, 10, 5, 16, 8, 4, 2, 1, - 9
13: 40, 20, 10, 5, 16, 8, 4, 2, 1, - 9
14: 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 17
15: 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 17
16: 8, 4, 2, 1, - 4
17: 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 12
18: 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 20
19: 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 20
20: 10, 5, 16, 8, 4, 2, 1, - 7
21: 64, 32, 16, 8, 4, 2, 1, - 7
22: 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 15
23: 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 15
24: 12, 6, 3, 10, 5, 16, 8, 4, 2, 1, - 10
25: 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 23
26: 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 10
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, - 111
28: 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 18
29: 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 18
30: 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 18
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, - 106
32: 16, 8, 4, 2, 1, - 5
33: 100, 50, 25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 26
34: 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 13
35: 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 13
36: 18, 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 21
37: 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 21
38: 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 21
39: 118, 59, 178, 89, 268, 134, 67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 34
40: 20, 10, 5, 16, 8, 4, 2, 1, - 8
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, - 109
42: 21, 64, 32, 16, 8, 4, 2, 1, - 8
43: 130, 65, 196, 98, 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, - 29
44: 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 16
45: 136, 68, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 16
46: 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 16
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, - 104
48: 24, 12, 6, 3, 10, 5, 16, 8, 4, 2, 1, - 11
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
50: 25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, - 24
BONUS-Can all whole numbers be traced back to one? Are you SURE?
yes ! at least all the numbers from 1 -> 1000000 can be set back to 1

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12-12-2004 07:20 AM  13 years agoPost 7
zacman

rrNovice

Scottsdale, AZ

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Yes, it is definitely 27 with 111 steps

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 = 111

noname: looks like you beat me to it.. i wrote a quick program to do it as well.

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12-12-2004 11:49 AM  13 years agoPost 8
Colibri

rrKey Veteran

The Netherlands

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1: 4, 2, 1, - 3
It is arguable that this one is wrong. When you start with 1 you're done.

Tim

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