Brain Teaser for the Geniuses???

Another example of how 18 can be the answer:

3 (the first square) times 4 (the second square) = 12

12 divided by 6 (the third square) = 2

2 times 9 (the fourth square) = 18.

This would be an abbreviated series alternating multiplication (with multiplication first) and division in a 3 operations series.

A more abstract way of thinking can create the answer of 24 (one of the answer choices and this cannot be disproven in logic):

3 (the first square) times 4 (the second square) = 12

12 times 6 (the third square) = 72

72 divided by 9 (the fourth square) = 8

8 times 3 (the first square) = 24

This is a multiplicative-multiplicative-divisional abbreviated series with a multiplicative reversion back to the first term.

Any student that answers 24 and can defend it with this logic should receive full credit. 18 has the most proofs, so far, however.

Another proof for 18:

3 (the first square) times 4 (the second square) times 9 (the fourth square) = 108

108 divided by 6 (the third square) = 18

This is an abbreviated multiplicative series with a "skip" that ends therefore with reverted division.

Naturally, the soundness of any answer is "why" and the proof. The human mind can provide no answer to any mathematics question without assumptions being made.

A more abstract way of thinking can create the answer of 21 (one of the answer choices and this cannot be disproven in logic):

a student can add the first two terms of a series (3 and 4 = 7) and multiply this sum by the first term (3) and arrive at 21. The next part of the series would involve adding the third and fourth terms of the series (6 and 9 = 15) and multiply it by the third term (6) and arrive at 90.

Once again, it is not the answer chosen, but the strength of proof(s). A student who chose this logic should receive full credit. 18 still has the most logical proofs.

A more abstract way of thinking can create the answer of 31 (one of the answer choices and this cannot be disproven in logic):

a student can add the first terms of a series (3 + 4 + 6 = 13) and add this to twice the fourth term of the series (9 * 2 = 18) and arrive at 31.

Once again, it is not the answer chosen, but the strength of proof(s). A student who defends his or her answer with this logic should receive full credit. 18 still has the most logical proofs.

My conclusion: there are infinite solutions to this problem, but by briefly reading this problem, 18 seems to be the best answer with the options provided.

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.

GT...it appears you are obsessing. No one said this problem was a perfect series. It is simply 5 squares that are all related somehow and we need to figure out what the fifth is. Based, once again, on the multiple choice answers we have to choose from, the answer is 18 because, again, it is a factor of 36 just like all the other squares.

It says NOWHERE that this is a perfect series we are working on. And....it also doesn't matter what the 6th square is. There is no sixth square. This puzzle has 5 squares.

The problem is set up to make one think, at first glance, that the answer is 13. Also, the 4 is there to throw things off. The problem is not a perfect series and was never said to be.

You can spend days working out various ways to come up with the various multiple choice answers. The fact is, none of them are logicial except the one I came up with!



[edit on 26-3-2007 by Excitable_Boy]

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

Hey, I would love to be able to ask the teacher for the answer, but this was the standardlize test. You know the end of the year test that everyone takes for hours and you circle those bubbles. I don't believe the teacher has the answers for those. They send them away to have them graded.

Originally posted 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.

GT...it appears you are obsessing. No one said this problem was a perfect series. It is simply 5 squares that are all related somehow and we need to figure out what the fifth is. Based, once again, on the multiple choice answers we have to choose from, the answer is 18 because, again, it is a factor of 36 just like all the other squares.

It says NOWHERE that this is a perfect series we are working on. And....it also doesn't matter what the 6th square is. There is no sixth square. This puzzle has 5 squares.

The problem is set up to make one think, at first glance, that the answer is 13. Also, the 4 is there to throw things off. The problem is not a perfect series and was never said to be.

You can spend days working out various ways to come up with the various multiple choice answers. The fact is, none of them are logicial except the one I came up with!

[edit on 26-3-2007 by Excitable_Boy]

Sorry but I am going to have to disagree as well. Any time I have ever seen a question with a series of numbers followed by a blank on a test, it has always been looking for a pattern. Besides that, following your method there is more than one right answer. The four squares are also all factors of 72, as is answer C (24). I believe the fact that the series adds in a pattern of +1, +2, +3 is too much to ignore. My vote is still for a misprinted answer key.

Excitable_Boy, I believe that you have the best proof of 18 (maybe I am wrong???) in a finite series.

I believe I have the best proof of 18 (maybe I am wrong???) in an infinite series.

Way to go, Excitable_Boy!!!

Originally posted by GreatTech
Excitable_Boy, I believe that you have the best proof of 18 (maybe I am wrong???) in a finite series.

I believe I have the best proof of 18 (maybe I am wrong???) in an infinite series.

Way to go, Excitable_Boy!!!

As I have shown above there would be more than one right answer with Excitable_Boy's method. As for yours I can only say that any of those methods would just be silly for the test makers to use on a standardized test, they are just random operations you applied to arrive at one of the multiple choice answers.

Just pretend for a moment that this wasn't a multiple choice question and a fill in the blank question instead. Then your methods would never arrive to a conclusion, it would be a wild guess. The only TRUE logical thing to do with this question is to look for a pattern.

Edit - Even besides everything I said above, look at the question itself. It isn't directing the student to find what the numbers have in common and then add in another number that fits, or to add random operations to the numbers to arrive at one of the multiple choice questions. It shows a sequence of numbers and is asking what comes next in the sequence.

[edit on 3/26/2007 by somedude]

Originally posted by GreatTech

The sequence is 3, 4, 6, 9, 18, 36, 108, 324, 1944, 11664...

The two keys are:

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.

somedude, in defense of 18 in a finite series, 18 is a factor of 36 AND 72, whereas 24 is only a factor of 72, not 36.

The answer of 13 is very logical, but since it is not an option, we have to think deeper. 13 would be the simplest correct answer in a non-multiple choice test.

Once again it depends on the quality and quantity of proofs.

Any question with a series of numbers is open to infinite answers. But with a restricted set of answers, as in a multiple choice test, we must operate on the logic of the possible answers.

I, too, thought of 24 being a factor of 72, but since 18 is a factor of 36 AND 72, it becomes 2 proofs versus 1.

Please attempt to disprove the logic in my quote above that proves that 18 is the correct answer in an infinite series.

The answer is 42.

It is the answer to life, the universe and everything.

thanks mojo. (what do i win).

[edit on 26/3/07 by mojo4sale]

Originally posted by GreatTech
Please attempt to disprove the logic in my quote above that proves that 18 is the correct answer in an infinite series.

The problem is there isn't any logic to it. You are finding random relations among the numbers that happen to reach one of the multiple choice answers by coincidence. If we had four completely different multiple choice answers, then you would probably just find some random relations to reach one of those.

The fact that it is multiple choice is the key issue here. For an answer to truly be logical, it needs to be reachable without a given selection of answers. Since that is not possible with your method, and that there would be no end to possible answers, there is no logic behind it. Only guessing.

I am aware that 13 is not one of the choices, but you also have to accept that it could very well be a misprint, and with what we currently know about the problem:
A. A logical answer to the problem is not one of the choices
B. Tests are not always going to be perfect
The most logical assumption here would be that it is a misprint.


[edit on 3/26/2007 by somedude]

The four squares are also all factors of 72, as is answer C (24). I believe the fact that the series adds in a pattern of +1, +2, +3 is too much to ignore. My vote is still for a misprinted answer key.

As GT already said.....18 and 24 are both choices, so that rules out 72 as being the number factored.

Stating that the answers are a misprint is illogical. My answer was quite logical.

A. A logical answer to the problem is not one of the choices
B. Tests are not always going to be perfect
The most logical assumption here would be that it is a misprint.

Wrong....a logical answer to the problem has been found. Get over it already. I agree with what you said about the various methods used by GT to get answers...they are simply taking the choices and finding random ways to come up with them. That's what my first two tries were.

But, for you to say that 18 isn't a logical answer is actually rather humorous at this point!

[edit on 27-3-2007 by Excitable_Boy]

You seem to be missing the point I made about how an answer is logical. To find a logical answer, work the problem out without a multiple choice selection. 13 is a logical answer because it falls in line with a pattern that is being displayed by the first 4 numbers.

Now even if we were to use your method, which doesn't really make sense in the first place because of how the question is presented, the next number in the series would be 12, not 18. This has been pointed out previously in the thread. It is not logical to skip a number when you are working with a series. Again 18 being there is just a coincidence, do you really think you would have put 18 as an answer if you were taking this test and it wasn't multiple choice?

[edit on 3/27/2007 by somedude]

Now even if we were to use your method, which doesn't really make sense in the first place because of how the question is presented, the next number in the series would be 12, not 18. This has been pointed out previously in the thread. It is not logical to skip a number when you are working with a series. Again 18 being there is just a coincidence, do you really think you would have put 18 as an answer if you were taking this test and it wasn't multiple choice?

A big part of the problem IS that it is multiple choice. It takes away the OBVIOUS answer of 13 and forces the test taker to think harder and outside the box.

You keep talking about a series. The problem doesn't. It doesn't say COMPLETE THIS SERIES anywhere. It shows 4 squares that relate and shows you 4 answers and you have to find the one that relates to the others. There is NO TALK anywhere about completing a series.....It wants YOU to look at the 4 choices for answers and find the one that RELATES to the others......no discussion of a series anywhere!!

They were put in this order: 3,4,6,9 for a reason. So that everyone would immediately jump to the conclusion that the answer is 13.

Given the same question, and with the four sguares in this order:

4,9,3,6..........the answer would STILL BE THE SAME...but, the problem wouldn't have the ability to fool the test taker into thinking that the answer is 13......

Move on please.....you're boring me.......

The answer........42

SportyMB

I'm sorry that someone that disagrees with you bores you, feel free to ignore what I say.

A big part of the problem IS that it is multiple choice. It takes away the OBVIOUS answer of 13 and forces the test taker to think harder and outside the box.

Think outside of the box? Is this a math question or a philosophy question? Last time I checked mathematics is systematic.

You are right that it doesn't specifically instruct the student to find the next number in the series, but.....

It wants YOU to look at the 4 choices for answers and find the one that RELATES to the others

it doesn't specifically instruct the student to do that either.

In my own experience with tests, which is all I really have, questions presented like this have a pattern to them and want you to fill in the next number of the series (I could very well be wrong). You speak as if you know what the test makers of the test were thinking when they made this problem, care to share your insight?

[edit on 3/27/2007 by somedude]

care to share your insight?

Care to move on?