Gomez solution

[boardy2002]

the difference goes 7,6,3,1,2,3,5

the adding/subtracting goes like this:-1,-3,-2,+1,+1,+2

so the next 5 numbers are 30,33,35,37,40

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Boardy2002

[CrystyB]

that post would belong in the solution Gomez puzzle topic.

But really, why "7,6,3,1,2,3,5,1,3,2,2,3..."? There's nothing special about that sequence to make it worth a puzzle!...

[frog]

When do we get the answer? I really need 2 no cos its killing me!

[Falcon]

Spoiler



Find the 2nd 9th 15thetc... words in the introduction, look at their initial letters. THe rest should become clear very quickly.

[Nauplius]

So using Falcons suggestion I get:

31, 37, 40, 42, 55

[Gifthorse]

Why do people submit these kinds of puzzles. Falcon You are a spoiler!!!

Why don't people just submit one thread instead of starting another?

See my solution in the other thread.

[Gifthorse]

This is probably wrong but I think the solution is . . .
dividing with primes

2,9,15,18,19,21,24,29. . . . . .27, 30, 39, 27, 30


How did I come up with this guess

We start with the Number 2

(9/2)= (4 Rem 1) = (5) x 3 = 15 then we let the next number be 18

(19/3)= (6 Rem 1) = (7) x 3 = 21 then we let the next number be 24

So when we do 29 we get. . . . .

(29/5) = (5 Rem 4) = (9) x 3= 27 then we let the next number be 30

This is where I get stuck, because I have to assume the next number to be 39


If thats true then when we devide by the next prime, which is 7, we get. . . . . .

(39/7) = (5 Rem 4) = 9 x 3 = 27 then we let the next number be 30


Its interesting to note that if we continue along with the sequence using only primes we get....

27,30, 39 ,27,30, 49, 27,30, 59, 33,36, 69, 15, 18, 79, 21,24, 89, 69,72,

99, 45,48

I MAY BE TOTALLY WRONG for instance my explanation doesn't explain the number 2 and its relevance although I did use it as my starting point for dividing

There is also the issue regarding transitions from a number to the numbers that end in 9.

Example (#)-> 9 (#) -> 19 (#) -> 29 I don't think my solution explains this part at all


I hope someone can shed more light on this. Also, what about normal counting numbers or using exponents.

Please reply

[Falcon]

What are you getting worked up about Gifthorse?

[The Unknown]

Well, board, I agree with your solution for the most part, but. I am not sure if it originally started out with 2 maybe they started out with 0+2=(2)+7=(9) but if even they did not, you forgot to put a 7 in too as it is the first thing you add into to get the next number so. Here is what i think it is, I never seem to be able to explain things in word form, so i will show you the equation. Note the numbers in () are the numbers from the sequence and the next five numbers:
(2)+7=(9)+7-1=(15)+ <<<this si where it gets a little tricky, it can either be 6 divided by 2 or 6 minus 3 but i will go with six minus three>>> (2)+7=(9)+7-1=(15)+6-3=(18)+3-2=(19)+1+1=(21)+2+1=(24)+3+2=(29) <<<so now assumeing thatyou start off with 7 it would be>>>
(2)+7=(9)+7-1=(15)+6-3=(18)+3-2=(19)+1+1=(21)+2+1=(24)+3+2=(29)+7=
(36)+7-1=(42)+6-3=(45)+3-2=(46)+1+1=(48)+2+1=(51)+3+2=(56)

i went on to 7 for fun, but the next five numbers are 36,42,45,46,48
mainly for the fact that that is the pattern the first 8 numbers went in and if they are repeating that is it. Or you can have fun and flip the signs to their opposite. or start from the back and go to the begining. But that is it 36,42,45,46,48 in my opinion is the right answer : P. Sorry if i posted in the wrong forum. If so can you point me in the right one?

[Gomez]

Falcon's got it. I hope you weren't too disappointed that it was a non mathematical sequence. I know they're not everyone's favourite. Just out of interest, did anyone like this puzzle?

[CrystyB]

Now that i know what this was about, it's very cute*! Anyway i must confess i missed Falcon's post. I think he should've bolded the *SPOILERS* part...

* But i hate it! It has 14 answers...

[This message has been edited by CrystyB (edited 07-06-2002 04:03 PM).]

[pixies]

I went far enough to be excited for a momment but i got stuck at the numbers 24,29
Well,what i did was:
(9)-(2)=7+ 8 = (15)
(15)-(9)=6+ 8+4 = (18)
(18)-(15)=3+ 8+4+4= (19)
(19)-(18)=1+ 8+4+4+4= (21)
(21)-(19)=2+ 8+4+4+4+4= (26) - while it should be 24 according to the posted sequence.

Whats the answer anyway?Does it have any meaning at all?

[Hitchhiker]

The answer is printed invisibly in Falcon's post, reply 3 of this thread. It is less mathematical and more instinctual.

[CrystyB]

Actually the answer isn't in there!

[Cz Kc]

Ha,Ha,Ha! What a fun and interesting puzzle! Thanks,everyone!

[Dave00]

I think I found an answer. If we take the Fibonacci sequence from the third progression (2) and we minus it from each respective progression of the Gomez sequence, we get the following:
{2,9,15,18,19,21,24,29}-{2,3,5,8,13,21,34,55}
=0,6,10,10,6,0,-10,-26
the difference between these is:
6,4,0,-4,-6,-10,-16
from the 10 onwards we can use the Fibonacci sequence to determine the next numbers. ((-4)+(-6)=-10, (-6)+(-10)=16)
We then get:
6,4,0,-4,-6,-10,-16,-26,-42,-68,-110,-178,-288
Since we used:
Gomez # - Fibonacci # = 6,4,0,-4,-6,-10,-16,-26,-42,-68,-110,-178,-288
We can then say that:
Gomez # = Fibonacci # - {6,4,0,-4,-6,-10,-16,-26,-42,-68,-110,-178,-288}

Thus we get 37,50,71,105,260!

(The first two numbers of the differences between the Gomez # can be ignored as it is just a reflection of the forth and fifth)

[CrystyB]

Yes, you found an answer. As i said before, There's nothing special about that sequence (6,4,0,-4,-6,-10,-16,-26,-42,-68,-110,-178,-288) to make it worth a puzzle!...

And Gomez could you please state which of the next was the intended solution?
31 37 40 42 55
31 37 40 48 55
31 37 40 51 55
31 37 40 53 55
31 37 46 48 55
31 37 46 51 55
31 37 46 53 55
31 37 49 51 55
31 37 49 53 55
31 45 46 48 55
31 45 46 51 55
31 45 46 53 55
31 45 49 51 55
31 45 49 53 55

[Gomez]

The first one.