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Sequence puzzle


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Go to solution Solved by rookie1ja,

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The below is a number puzzle. It should be read left to right, top to bottom.

Question 1 What is the next two rows of numbers.

Question 2 How was this reached.

1 1

2 1

1 2 1 1

1 1 1 2 2 1

? ? ? ? ? ?

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It's secret is to say whay you see on each line and what you see becomes the next line. For full answer see below.

Line 1 is "Two ones" (2 1)

Line 2 then becomes "One two, and one one" (1 2 1 1)

Line 3 therefore is "One one, one two and two ones" (1 1 1 2 2 1)

Line 4 is "Three ones, two twos and one one" (3 1 2 2 1 1)

Line 5 is "One three, one one, two twos and two ones" (1 3 1 1 2 2 1 1)

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1

11

21

1211

111221

312211

13112221

1113213211

31131211131221

13211311123113112211

11131221133112122113212221

3113112221232112112221312113211

13213213211121312211221321112111221131221

1113121113123112111311222122111312311231222113112211

31131112311312132112311321321122311311121321121311322113212221

13211331121321131112131221121321131211131221221321133112111312211211132113222113

12113211

11131221232112111312211331121113112221121113122113111231131122112211131221232312

3113112221123113122113322113111221131221

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I thought of a puzzle based on this topic, so I'm posting it here. What is the next number in this sequence?

421

2

488

504

421

?

Trying to figure this out away from the computer will probably not help you.

The sequence is not defined mathematically.

The sequence is finite, and it is within your power to change later numbers in the sequence, although not the next one.

The first sentence my original posting is a clue.

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Is it 1 3 1 1 2 2 1 1? The same as the other one? I did this without any thinking, just using the clues. Although i believe those were there just to confuse us right?

No to all three questions. The pattern in the sequence that I posted would be very hard to figure out without looking at any of the clues that I posted. I may post more clues later.

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My next clue is to expand the original riddle by giving you more of the sequence. Reread the other clues if you like, it may help you.

The following is a sequence that is based on this topic. What is the next number in this sequence?

421

2

488

504

421

113

421

113

3933

3375

4154

4000

1216

4000

4000

4219

4000

4219

4000

?

Sorry if this is a stupid sequence and the answer ends up making you groan, but I thought of it so I figured I'd give it a try.

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there is a slight alternative

1 1

2 1

1 2 1 1

3 1 1 2

....

go figure

I have not seen this version before and it intrigued me. (Actually I think there is a minor error in the second line: 1211 should be 1112) I have studied the other version and it goes on indefinitely and the largest digit is a three (3). However, this version, when continued, differs in two significant ways:

1. It is finite (i.e. it starts to repeat)

2. The largest digit is a four (4)

Here's the whole sequence:

1

11

21

1112

3112

211213

312213

212223

114213

31121314

41122314

31221324

21322314

21322314

The generic pattern is: a1b2c3d4, where a, b, c, d are the total number of occurrences of the digits 1, 2, 3, and 4 in the previous line.

Thanks for this new way of looking at an old problem!

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My next clue is to expand the original riddle by giving you more of the sequence. Reread the other clues if you like, it may help you.

The following is a sequence that is based on this topic. What is the next number in this sequence?

421

2

488

504

421

113

421

113

3933

3375

4154

4000

1216

4000

4000

4219

4000

4219

4000

?

Sorry if this is a stupid sequence and the answer ends up making you groan, but I thought of it so I figured I'd give it a try.

[/quote

IS THAT 4323

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The below is a number puzzle. It should be read left to right, top to bottom.

Question 1 What is the next two rows of numbers.

Question 2 How was this reached.

1 1

2 1

1 2 1 1

1 1 1 2 2 1

? ? ? ? ? ?

An alternate solution:

Given that the first three are starting conditions, then the fourth line could be: 21111211

Explanation:

* The last two digits alternate between 11 and 21

* The first two digits, in the first three sequences repeat

* Interior numbers are shifted right

Hence the next number would be: 1221111221

Ta da!

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Ano, I love this problem! ^_^

"The below is a number puzzle. It should be read left to right, top to bottom.

Question 1 What is the next two rows of numbers.

Question 2 How was this reached.

1 1

2 1

1 2 1 1

1 1 1 2 2 1

? ? ? ? ? ? "

3 1 2 2 1 1

Ano, now to explain...

Ano, first, seperate the number sequence into groups of numbers based on what number they are, for example '1 1 1' '2 2' and '1'. Then, take the total number of numbers in the first group -there's 3 ones, so we use 3- and then put what number was counted -in this group, 1-, and repeat with the remaining numbers.

Ano, the next line would be '1 3 1 1 2 2 2 1', following the same process as above...

Ano, this is a rather old puzzle, and I've seen it several times in books, school newspapers, and on the internet....

Edited by fireprincess59
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