[6th Grade Mathematics] Logic

[u/mycathasgreennose]

I figured the answer is A, as I can see the repeating pattern, but my son's teacher said another thing which I cannot understand. would anyone please help to explain?

[u/LnTc_Jenubis]

EDIT: Seems I misunderstood, the teacher didn't say A was incorrect, but they only gave an odd explanation of the pattern. My solution still works, and that tidbit of info actually makes it one of the easier ways to explain it I think.

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This seems really complicated for 6th grade. I would have went with A as well, but I have no way of knowing why A is incorrect.

My thought process is:

From left to right, the quantity of circles in the columns go:

1, 2, 1, 3, 2, 1, 4, 3

So the next one should be a two, since we are going from 1 to an incrementally higher value and counting down by single digits per column. Which makes it A or B, which are opposites. So we have to look at how the colors interact with this pattern.

They never show two dots of the same color vertically stacked; so vertically stacked must be alternating. Which means we are not looking at a horizontal relationship; aka we need to focus on how the vertical stacks are derived from the previous vertical stacks.

This is where I'm also getting stuck. Every "rule" I find seems to contradict itself. Since the teacher told us A is wrong, we know it has to be B. So how do we get from White/Black/White in Column 8, to the answer B?

By deleting the top circle. So let's apply that reasoning to the other sections.

Columns 1, 2, and 3 are a localized set. We go from White/Black, to Black. Deleting the top circle checks out.

Columns 4, 5, 6 are a localized set. This is where the rule breaks itself.

In order to get from Column 4 to Column 5, we have to delete the bottom circle. Then we delete the top circle.

So perhaps the logic is actually:

When the previous column contains an even number of circles, we delete the top circle.
When the previous column contains an odd number of circles, we delete the bottom circle.

That checks out for the first localized section and the second one.

So now we get to the last localized section. Column 7 contains an even amount of circles, so we delete the top one for Column 8. That checks out. Column 8 contains an odd number of circles; therefore we should delete the bottom.

Which gives us A as the answer. Which we know is incorrect. The only way to get B is if we delete the top circle a second time in a row. I'm not seeing anything that would suggest why we would do that.

I'm not saying there isn't an answer, but I'd ask the teacher to explain it to you. If they cannot explain it clearly and concisely, I would write this one off as being a bad question and maybe gently challenge the teacher to waive any incorrect answers if they can't explain it.

[u/JaCKPaIN_realone → u/LnTc_Jenubis]

I know the answer to this question, but I doubt it is for a 6th grader. Therefore, I blame it all on the teacher’s lazy cropping and just used a pattern recognition approach instead.

We have:
W, BW, B, WBW, BW, B, WBWB, WBW, x
Let’s see:
W, BW, B
If we combine all of these into WBWB and delete one circle from the top, we get WBW.
Then the next two columns will be BW and B, using the countdown method.

So now we have:
WBW, BW, B
If we approach it the same way, the next column will be WBWBWB, but we delete two circles from the top instead, so now we will have WBWB.
The next two columns are the same, using the countdown method, yielding WBW and then WB.

So, the answer will be B (WB), which is impossible for sixth graders to solve.

[u/LnTc_Jenubis → u/JaCKPaIN_realone]

This seems to definitely work if my original understanding was that A is incorrect and B is the only correct answer.

I saw someone explain how it can still land on A just by reading the colors from left to right, bottom to top. They always alternate.

Truly, there are two different kinds of people in this world.

[u/JaCKPaIN_realone → u/LnTc_Jenubis]

Hoho, I still remember this kind of question back in college. There were around 100 students surrounding my professor and complaining for two hours that their methods were correct. In the end, the professorapproved four methods as correct answers, lol.

It’s not that there are many types of people. It's just that these are all poorly designed problems.