Brain Teaser for the Geniuses???

Originally posted by GreatTech
The sequence is 3, 4, 6, 9, 18, 36, 108, 324, 1944, 11664...

The two keys are:

***

Shar, please provide us with the answer and proof.

[edit on 22-3-2007 by GreatTech]

It makes sense what you're saying - both keys... BUT the "keys" you're giving isn't derived from the 4 given numbers.

For your first key... What is 3 the square off? And the 6? If they followed that series of numbers, as you suggest, then they would have had to begin with 2,3,4,9... etc. for it to make sense.

For your second key... It makes perfect sense if you look at your complete series. But again, the given series is too short (holds too little information) to derive the pattern. (Ex. 3,4,6,9,18 - at least)

Interesting enough, if this series started with 1,2,3,4,6,9... etc. it would have been the "Narayana series" - a type of delayed Fibonacci series - where the series would be 1 2 3 4 6 9 13 19 28 41...

I have to agree with all the rest. 13 is the obvious answer. If a bunch of "wise ass" adults can't "break the code" (I'm assuming that some of the posters in this thread are adults), how could a child get the answer - not wanting to insult children... I'd have to say that the answer options were incorrect. If it's not then we have no choice but to use GreatTech's formula, which would mean that this is indeed a "brainteaser for geniuses" and not really for kids... (Make of that what you want, GreatTech )

I think the answers 14

3 4 6 9

(3) + (4) -1 (6) 4 + 6 -1 (9) 6 + 9 -1 (14)

oh I just saw what the choices were... so it can't be what I came up with... hmm



[edit on 23-3-2007 by NJE777]

I think the answer is 13 for non-geniuses and 14 for geniuses.

j/k.......I'm still going with 14.

Damnit someone give me the correct freakin' answer please!!!!!

Peace

1) The second square (4) is the numerical square of 2. The fourth square (9) is the numerical square of 3. The sixth square (36) is the numerical square of 6, derived from the numerical square of square 2 (2) multiplied by the numerical square of square 4 (3), or (2*3)^2 = 36. The eighth square (11664) is the numerical square of 108, derived from the numerical square of square 4 (3) multiplied by the numerical square of square 6 (36), or (3*36)^2 = 11664. This can continue on indefinitely.

2) The second key is much simpler. An alternating odd sequence can be partly proven since the first square (3) times the third square (6) equals one of the answer choices (18). This can continue on indefinitely. This second key combined with the first key provides a logical answer of 18.

GT...great work here. But, I'm not convinced with either 1 or 2. At first glance, 1 looked good. But, you assume that the square before 3 is 2. 2nd, you do nothing with 4, as in 4x4 is 16 which is not in the series. Plus, where does 18 come from? There's no solid number squared that equals 18. In this line of thinking, the 5th square should be 16....and we know it can't be!

Your second choice is just a guess....no logic behind it.

My son says this is not logical. He seems to say your using just random variables. Any number can do that. Where does the 2 and 9 come from is his question?

It's quite logical. The 2 and the 9 are variables used for the series. They are not random. Where do the 2 and 9 come from? From the person that created the problem!

The answer is 31 add up all the squares, the last box should have 4 in it.

3+1+4+1+6+1+9+1+4+1=31

3+1+4+1+6+1+9+1+4+1=31

Wrong.....in your solution here, the 5th box is 4. 31 is the 6th box. The answer needs to be the fifth box....sorry!



[edit on 24-3-2007 by Excitable_Boy]

I would say the difference is 1,2,3,4 thus = 13 (misprint)

though what level of education is this? Okay I just read the thread seems like your son knows about variables so this sequence is too easy
This is fun i am gonna ponder dis.

[edit on 24-3-2007 by Selmer2]

Excitable sorry but your wrong, its about what do you see, and it is:

1sq containing three sq's

1sq ditto 4 sqr's

1sq ditto 6 sqr's

1sq ditto 9 sqr's

1sq blank

So you have 4 sqr's containing 22 sqr's plus 1 blank sq = 27

if the available answers are 18, 21, 24, or 31 then the last sq can only hold 4, 4=27=31

I throw away everything I have said until this point. I have the answer. This is correct: It is 18 after all. Why?

Because all the numbers are factors of 36!!

36/3 = 12
36/4 = 9
36/6 = 6
36/9 = 4
36/18 = 2

The answer is 18 baby!! THANK YOU!!




[edit on 24-3-2007 by Excitable_Boy]

Good stuff

makes perfect sense

Originally posted by Excitable_Boy
I throw away everything I have said until this point. I have the answer. This is correct: It is 18 after all. Why?

Because all the numbers are factors of 36!!

36/3 = 12
36/4 = 9
36/6 = 6
36/9 = 4
36/18 = 2

The answer is 18 baby!! THANK YOU!!




[edit on 24-3-2007 by Excitable_Boy]

You should win a million dollars!!

Excitable_Boy, you are a genius. However, would not your logic dictate that the series (beginning with 3) is composed of factors that would have 12 as the fifth square? Why is 12 skipped?

We both agree that 18 is the answer for the fifth square, but for different reasons.

What is your series after 18?

[edit on 25-3-2007 by GreatTech]

Excitable_Boy


Thankyou. Yes, that is the first thing that makes sense to me. Seems to be the correct answer.

Excitable_Boy, you are a genius. However, would not your logic dictate that the series (beginning with 3) is composed of factors that would have 12 as the fifth square? Why is 12 skipped?

12 is skipped because it is skipped. It is a multiple choice answer. 12 is not one of the answers, but 18 is. 2 and 1 are also skipped......so?

All the factors of 36 are: 1,2,3,4,6,9,12,18,36

So...some are skipped. All the squares are factors of 36.....that is the connection.


And Shar...you are welcome!!

Peace!!




[edit on 25-3-2007 by Excitable_Boy]

You know if that is it, That is so hard. Look how long it took people here on boards to get the answer. Wow, these test today.

You know if that is it, That is so hard. Look how long it took people here on boards to get the answer. Wow, these test today.

I said the same thing to my wife. But we are also not in school every day doing math. The answer would have come quicker if it was something I was doing all the time.....

To Excitable_Boy

Originally posted by Excitable_Boy

Excitable_Boy, you are a genius. However, would not your logic dictate that the series (beginning with 3) is composed of factors that would have 12 as the fifth square? Why is 12 skipped?

12 is skipped because it is skipped. It is a multiple choice answer. 12 is not one of the answers, but 18 is. 2 and 1 are also skipped......so?

All the factors of 36 are: 1,2,3,4,6,9,12,18,36

So...some are skipped. All the squares are factors of 36.....that is the connection.


And Shar...you are welcome!!

Peace!!

[edit on 25-3-2007 by Excitable_Boy]

Excitable_Boy, I hate to be argumentative (the only things I enjoy in life are love and peace!!!), but would not logic dictate that you cannot "skip" in the middle of a series (its core), but you can before and after the series.

I believe that we are both correct with 18, but we have different reasons.

Again, what is your series after 18?

Shar, please ask your son's teacher for the answer and the proof.