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 Mister Logic
Joined: 3/5/2009
Msg: 1
A Simple Puzzle Question...Page 1 of 3    (1, 2, 3)
For those of you who enjoy solving math puzzles, what are the next three numbers in the following sequence:

4, 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, ?, ?, ?

(Since there may be more than one "correct" answer to this problem, be prepared to explain how you got your answer.)
 JustDukky
Joined: 7/8/2004
Msg: 2
A Simple Puzzle Question...
Posted: 5/25/2009 4:58:33 PM
I agree with greg14229

These things are simply fun! While this MAY not be the appropriate forum for them (if another more suitable forum exists -- I haven't checked), but hell, as long at it doesn't get cluttered with them, what's the harm?
 Mister Logic
Joined: 3/5/2009
Msg: 3
A Simple Puzzle Question...
Posted: 5/25/2009 5:12:07 PM
I've always thought that mathematics was a part of science, just as religion is a part of philosophy. (And there are sure a lot of religious threads in this forum. And THEY seem to be acceptable to the moderators!)
 wvwaterfall
Joined: 1/17/2007
Msg: 4
view profile
History
A Simple Puzzle Question...
Posted: 5/25/2009 7:29:57 PM
I keep thinking the numbers represent some sort of intervals, but darned if I can figure out intervals between what.

It also seems like I remember a "no games" rule somewhere in the list of forum rules, so that might have explained the votes for deletion, but I could be mistaken on that.
 letscnow
Joined: 5/10/2008
Msg: 5
A Simple Puzzle Question...
Posted: 5/25/2009 7:39:20 PM
We need more than that to help you solve this problem. We cannot get a steady pattern from the numbers, order you provided. If we tried 3, 4, 5 numbered sets, we would end up with more numbers than you asked for.
 insert user name
Joined: 5/4/2006
Msg: 6
A Simple Puzzle Question...
Posted: 5/25/2009 7:49:43 PM
If the pattern holds, the answer is 3, 5, 4
 Mister Logic
Joined: 3/5/2009
Msg: 7
A Simple Puzzle Question...
Posted: 5/25/2009 11:57:27 PM
The sequence that I have in mind does NOT continue with 3, 5, 4.
Instead, the next three numbers in the sequence are 6, 6, 8:

Now, what are the NEXT three numbers in my sequence:

4, 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, ?, ?, ?
 hyoid
Joined: 5/12/2009
Msg: 8
A Simple Puzzle Question...
Posted: 5/26/2009 5:46:33 AM
if you continue the original sequence with 6,5,4; then the sum of the 3 digit groups proceding from the left read as follows:

10 11 12 13 11 12 13 14 12 13 14 15

continue the sequence with 4,6,5,5 to get the 13 14 15 16 series
 Vancer
Joined: 10/29/2006
Msg: 9
A Simple Puzzle Question...
Posted: 5/26/2009 6:33:04 AM
I kinna guess the pattern in the sequence.
But I can tell you that if you put it into a midi player, and play the tune using a grand piano sound effect, it sounds like creepy 80's horror music.
Like the killer is chasing the main character through a hallway.
 Mister Logic
Joined: 3/5/2009
Msg: 10
A Simple Puzzle Question...
Posted: 5/26/2009 10:51:42 AM

if you continue the original sequence with 6,5,4; then the sum of the 3 digit groups proceding from the left read as follows:

10 11 12 13 11 12 13 14 12 13 14 15

continue the sequence with 4,6,5,5 to get the 13 14 15 16 series

Hmm... an interesting solution for the original sequence. (As I had said, "there may be more than one 'correct' answer to this problem". Congratulations on finding one of them!)

But as you now know, the sequence that I had in mind actually continues with 6, 6, 8:

4, 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, ?, ?, ?

What are the NEXT three numbers?

[HINT: The sequence is generated by a very simple 2-step process.]
 Mister Logic
Joined: 3/5/2009
Msg: 11
A Simple Puzzle Question...
Posted: 5/26/2009 12:20:23 PM
There have been several posts in this thread that have given "3,5,4" as the next three numbers. So I guess that answer could be accepted as a legitimate answer to the sequence that was originally posted. (I even said, "There may be more than one 'correct' answer to this problem".) But as I indicated in post #14, that original sequence should have included three more terms: 6, 6, 8. The sequence that I had in mind is actually:

4, 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, ?, ?, ?

(I wish there was some way for me to go back an modify my original post, but it's too late now. )
 Mister Logic
Joined: 3/5/2009
Msg: 12
A Simple Puzzle Question...
Posted: 5/26/2009 10:51:32 PM
^^^^^ Congratulations on finding the answer!


I'm guessing the OP is a programmer .

Among other things.
 Mister Logic
Joined: 3/5/2009
Msg: 13
A Simple Puzzle Question...
Posted: 5/27/2009 9:54:26 AM

[HINT: The sequence is generated by a very simple 2-step process.]

Simple Step #1: Write down each integer as a word (i.e., ZERO, ONE, TWO, etc.)

Simple Step #2: Count the number of letters in each of those words.
 wvwaterfall
Joined: 1/17/2007
Msg: 14
view profile
History
A Simple Puzzle Question...
Posted: 5/27/2009 10:17:36 AM
I didn't pay any attention to the number of steps, figuring it would turn out like it did - that you could make the process any number of steps that suits you:

One step process: count the number of letters in each integer written in english, starting with zero.

Or.....

Pick up pencil

sharpen pencil.

write the number "zero"

Count the number of letters in "zero"

write down the result

Write the number "one"

etc.....

These kinds of puzzles are kinda like those pictures with hidden images in them. Sometimes they leap right out at you, sometimes they seem invisible until pointed out. Always fun, though...
 Mister Logic
Joined: 3/5/2009
Msg: 15
A Simple Puzzle Question...
Posted: 5/27/2009 4:57:48 PM
^^^ How about: 17, 19, 18 , ... etc.
 chrono1985
Joined: 11/20/2004
Msg: 16
A Simple Puzzle Question...
Posted: 5/27/2009 5:08:01 PM
5, 4, 4

My logic
First the number is evaluation twice with the same function, then the next group of 3 has it's first as evaluation once of a function. So it follows a pattern of repeating -1 or -2 depending on how many iterations of the function have been evaluated resulting in a crescendo rythm of pulse, modify, repeat, pulse-modify, modify, repeat, etc

at the last given 3 {5, 4, 3} it goes +2, -1, -1, so following the logic of the algorithm I mentioned above the next logical series is +2, -1, -1. The last given two however break the rythm so it leads me to believe I have a bug in my logic somewhere.
 hyoid
Joined: 5/12/2009
Msg: 17
A Simple Puzzle Question...
Posted: 5/28/2009 1:59:18 PM
if you continue the original sequence with 6,5,4; then the sum of the 3 digit groups proceding from the left read as follows:

10 11 12 13 11 12 13 14 12 13 14 15

continue the sequence with 4,6,5,5 to get the 13 14 15 16 series

Hmm... an interesting solution for the original sequence. (As I had said, "there may be more than one 'correct' answer to this problem". Congratulations on finding one of them!)

But as you now know, the sequence that I had in mind actually continues with 6, 6, 8:


I had only read your original post when I came up with my solution.

I was sure mine was correct . The first nine sums fit the pattern. That seemed way too unlikely for chance.

Turns out it was not.
 Mister Logic
Joined: 3/5/2009
Msg: 18
A Simple Puzzle Question...
Posted: 7/4/2009 9:59:27 AM
There is a boat that only holds a maximum of 3 people.

A dog is not a person. And so I assume that a dog doesn't count as part of the boat's maximum cargo (since you didn't indicate otherwise). So three river crossings will do it:

1 - Three men and their respective dogs (one of which is the "driver dog") cross the river.

2 - The "driver dog" and his owner go back and pick up the remaining passengers.

3 - The final crossing is made.

(I'm sure that this is not what you had in mind. But given the problem as it was stated, this "solution" is certainly a valid one. )
 Mister Logic
Joined: 3/5/2009
Msg: 19
A Simple Puzzle Question...
Posted: 7/4/2009 11:30:29 AM

ONE dog is trained to drive the boat.

Does this mean that ONLY that dog (and nobody else) is allowed to drive the boat?
 Super Ryan
Joined: 9/15/2007
Msg: 20
A Simple Puzzle Question...
Posted: 7/4/2009 11:36:27 AM
Here's a riddle-

5 people and their 5 dogs are trying to cross the river.

Let's name all the men 1,2,3,4,5, the dogs A,B,C,D,E and the ownership is 1A,2B,3C,4D,5E. And we will say they start on the west bank and need to get to the east bank.

Trip:
1. W-E A and B
2. E-W A
3. W-E 1,2 and A
4. E-W 1 and A
5. W-E A and C
6. E-W 2
7. W-E 2 and 3
8. E-W A
9. W-E 1,4 and 5
10. E-W 1
11. W-E 1 and A
12. E-W A
13. W-E A, D and E

What's my prize?
 Super Ryan
Joined: 9/15/2007
Msg: 21
A Simple Puzzle Question...
Posted: 7/4/2009 5:52:15 PM
plus on move 5, you left dogs a AND c without their owners

In move 5, dogs A and C are in the boat without people.

but when they get to the other side, they are alone with person 2

When they arrive, person 2 hops in the boat and leaves.
 Super Ryan
Joined: 9/15/2007
Msg: 22
A Simple Puzzle Question...
Posted: 7/4/2009 7:40:38 PM
Ok, I was under the impression that the dogs would not attack when loading and unloading the boat.
So I have another answer.
________________________________________________________

Let's name all the men 1,2,3,4,5, the dogs A,B,C,D,E and the ownership is 1A,2B,3C,4D,5E. And we will say they start on the west bank and need to get to the east bank.

Trip:
1. W-E ABC
2. E-W A
3. W-ADE
4. E-W A
5. W-E 234
6. E-W 4D
7. W-E 1A
8. E-W 3C
9. W-E 345
10. E-W A
11. W-E ACD
12. E-W A
13. W-E AE

Still 13 trips.
 Mister Logic
Joined: 3/5/2009
Msg: 23
A Simple Puzzle Question...
Posted: 7/5/2009 11:39:56 AM
A QUESTION ABOUT THE RULES: Suppose a dog is in the boat, and a man waiting on the shore is not that dog's owner. When the boat arrives, will the dog attack the man? Or are they allowed to "swap places" quickly enough so that the man can drive safely away?
 Mister Logic
Joined: 3/5/2009
Msg: 24
A Simple Puzzle Question...
Posted: 7/5/2009 11:05:54 PM
A QUESTION ABOUT THE RULES: Suppose a dog is in the boat, and a man waiting on the shore is not that dog's owner. When the boat arrives, will the dog attack the man? Or are they allowed to "swap places" quickly enough so that the man can drive safely away?
yes, the dog will attack man if owner not there

If "swapping places quickly" is not allowed, then I can't solve the puzzle with fewer than 13 trips.
(If "swapping places quickly" WERE allowed, then I could have solved the puzzle with 11 trips.)
 Rainsands
Joined: 1/9/2007
Msg: 25
A Simple Puzzle Question...
Posted: 7/6/2009 2:35:31 PM
Let's name all the men A, B, C, D and E, the dogs a, b, c, d and e and the ownership is Aa, Bb, Cc, Dd and Ee. Dog a is the dog able to drive the boat. NS is near shore and FS is far shore.

1. From the starting shore dogs a, b and c cross. ( NS - A, B. C. Dd, Ee ....FS - a, b, c )
2. Dog a returns. ( NS - Aa, B, C, Dd, Ee ...FS - b, c )
3. Dog a takes dog d to the far shore. ( NS - A, B, C. D. Ee ......FS - a, b, c, d )
4. Dog a returns alone. ( NS - Aa, B, C, D, Ee ....FS - b, c, d )
5. Men B, C and D cross the river. ( NS - Aa, Ee ................FS - Bb, Cc, Dd )
6. Man B and dog b return to the starting shore ( NS - Aa. Bb. Ee ..........FS - Cc, Dd )
7. Man A drives dog a across the river. ( NS - Bb, Ee.................FS - Aa, Cc, Dd )
8. Man D and dog d return. ( NS - Bb, Dd, Ee...........FS - Aa,Cc )
9. Men B, D and E cross the river. ( NS - b, d, e.................FS - Aa, B, Cc, D, E )
10. Dogs a returns ( NS - a, b, d, e.............FS - A, B, Cc, D, E )
11. Dogs a, b and d cross the river. ( NS - e.......................FS - Aa, Bb, Cc, Dd, E )
12. Man E returns ( NS - Ee....................FS - Aa, Bb, Cc, Dd )
13, Man E and his faithful mutt e cross the river ( NS - Clear....FS - Aa, Bb, Cc, Dd, Ee )

Well, I too get 13 steps. There may be a duplication in there somewhere but no dog is left with a master other than his own.
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