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## 10 posts in this topic

Posted · Report post

:twisted:

Heres a number puzzle. Warning: this puzzle is fiendishly hard.

Here is a sequence of numbers:

1,2,3,2,1,2,3,4,2,1,2,3,4,3,2,3,4,5,3,2,3,4,5,4,3,4,5,6,4,3,4,5,6,5,4,5,6,7,5,2,

what is the next number in the sequence?

what is the 999th number in the sequence?

Hint: think outside the box

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Posted · Report post

101

but then I'm also thinking the 40th (your last one) should be 4 and that the next one should be 5. That's the only one that doesn't fit the pattern I've come up with.

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Posted (edited) · Report post

101

but then I'm also thinking the 40th (your last one) should be 4 and that the next one should be 5. That's the only one that doesn't fit the pattern I've come up with.

Sorry no but nice try... how did you get those numbers anyway? remember "Think outside the box"

Edited by matthew laming
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Posted · Report post

sigh. hoping I was right so you can explain it. but here

goes...

For each term X, subtract the corresponding number in the following sequence (which is really composed of two sequences).

Each number that is the Jth term follows one pattern while all others (I'll call Kth terms) follow a similar pattern. J is a number where (J+1)/5 leaves no remainder. ie 4, 9, 14 etc.

The first (Kth terms) sequence starts with 0, the second (for the Jth terms) starts with 2. Repeat the number until you alternate from a J term to a K term or back to a J term. When you switch term type add 4 or 5 to the last number in the sequence. If you added 4 the last time you switched term type, this time add 5 and vice versa. The first time you switch back to a K-type add 4. The first time you switch back to a J-type add 5.

So we have

0,

0,

0 (terms 1-3 K-type),

2 (term 4 J-type),

4 (term 5 K-type add 4 to last number in K sequence),

4,

4,

4 (terms 6-8 K -type repeat),

7 (term 9 J -type add 5 to last number in J sequence),

9 (term 10 K-type add 5 to last number in K sequence),

9,

9,

9 (terms 11-13 K-type repeat)

11 (term 14 J-type add 4 to last number in J sequence),

13 (term 15 K-type add 4 to last number in K sequence),

etc.

{Also could say "1st term is 0. Add Z to last term if term type switches, ow repeat where Z is 2,2,3,2,2,2,3,2,2,2,3...}

This sequence is 0,0,0,2,4,4,4,4,7,9,9,9,9,11,13,13,13,13,16,18,18,18,18,20,22,22,22,22,25,27,27,27,27,29,31,31,31,31,34,36,36... <--- where my bugaboo is.

So taking the counting numbers 1-40 and subtracting the above sequence we get

1-0 = 1

2-0 = 2

3-0 = 3

4-2 = 2

5-4 = 1

6-4 = 2

7-4 = 3

8-4 = 4

9-7 = 2

.

.

.

39-34 = 5

40-36 = 4 <--- the only number in my sequence that does not match yours.

41-36 = 5

Plugging a formula into Excel I get 999th term is 101.

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Posted (edited) · Report post

ha ha i like that. Heres a hint.

[spoiler=hint ]831st = 8

3888th = 15

3889th = 13

Edited by matthew laming
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Posted (edited) · Report post

I'm probably far off but is the next number in sequence 1 and the 999th 2?

edit/ I just read your hint after posting and believe I'm incorrect now

Edited by wolfcry911
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Posted · Report post

I'm probably far off but is the next number in sequence 1 and the 999th 2?

edit/ I just read your hint after posting and believe I'm incorrect now

no im afraid,

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Posted · Report post

I cheated a little, but

XLI --> 3

CMXCIX --> 6

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Posted · Report post

I cheated a little, but

XLI --> 3

CMXCIX --> 6

Yeah thats it! well done!

How'd you cheat?

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Posted · Report post

Yeah thats it! well done!

How'd you cheat?

I gave him the answer. J/K

Darn that last two!!

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