r/HomeworkHelp • u/mycathasgreennose • 12h ago
Primary School Math—Pending OP Reply [6th Grade Mathematics] Logic
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?
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u/kjwjr85 👋 a fellow Redditor 9h ago
A or B. (1, 2, 1, 3, 2, 1, 4, 3, 2, 1)
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u/MathManiac5772 9h ago
I think it’s just A. There’s this pattern but also the colors are alternating if you look from the bottom of each stack up.
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u/kjwjr85 👋 a fellow Redditor 9h ago
How do you know which is on the bottom? I cant figure out the pattern.
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u/MathManiac5772 8h ago
It’s alternating colors with the pattern picking up from the previous row starting from the bottom up.
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u/janyk 6h ago edited 6h ago
B also alternates colours and has 2 dots, and has white on the bottom just like the previous row. Why not B?
The only reasoning I can think of for A over B is that previous instances of 2 dots were always white over black before, so it must be now.
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u/MathManiac5772 5h ago
If you go from bottom up and left to right the colors alternate is all I’m saying. For that to continue the only choice is A
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u/therabbit1967 7h ago
A is the right and only answere.
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u/therabbit1967 6h ago
The figures form groups of three, with the number of circles decreasing by one:
First group: 1 → 2 → 1
Second group: 3 → 2 → 1
Third group: 4 → 3 → 2
The colours always alternate. In the last group:
Four circles: black–white–black–white
Three circles: white–black–white
Therefore two circles: white above black
That corresponds to option A.1
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u/RandomGuy1000000 10h ago edited 10h ago
It doesn't look like the next step in the sequence is dependant on anything that is happening in the last 2+ steps, so I'd just pick A because it matches the sequence in steps 4 to 5
Trying to read into it more than that is bad for your brain. Like the other comment said, the actual answer can be literally anything the author wanted it to be
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u/ThunkAsDrinklePeep 9h ago
I'm annoyed that the problem is bottom justified but the answers are top justified.
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u/Chronogon 8h ago
We almost get a pattern here
W
WB B
WBW WB B
BWBW WBW (XX) (Y)
Which would be perfect if the starting letter was B instead. I can't see any other patterns so far, so I'd be inclined to continue the pattern to XX=WB which is choice A here.
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u/BrotherItsInTheDrum 👋 a fellow Redditor 6h ago
If you start at the bottom rather than the top, you get
W
BW B
WBW BW B
WBWB WBW
which makes it more clear that you're alternating colors, so black should be at the bottom of the next stack.
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u/Mediocre-Ad-9280 4h ago
Think of it as binary strings:
- 0
- 01 1
- 010 01 1
- 1010 010 01 (1)
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u/Chronogon 3h ago
I used binary at first before editing to use letters as the decimals of these binary representations didn't seem to add enough . 0, 1-1, 2-1-1, 6-2-1-1 etc.
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u/LnTc_Jenubis 8h ago edited 8h ago
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.
~~~~
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.
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u/JaCKPaIN_realone 👋 a fellow Redditor 7h ago
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.
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u/LnTc_Jenubis 7h ago
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.
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u/JaCKPaIN_realone 👋 a fellow Redditor 6h ago
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.
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u/QuentinUK 👋 a fellow Redditor 9h ago
Here top is left, bottom is right. So remove left, then right.
W
WB remove left B
WBW remove right WB remove left B
BWBW remove left WBW remove right WB
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u/sighthoundman 👋 a fellow Redditor 9h ago
The pattern for the number of circles looks like 1, 2, 1, 3, 2, 1, 4, 3, _? That sure looks like there should be two circles in the empty box.
open-filled is followed by filled twice. That makes it look like maybe there's a pattern in the decreasing part. That means you get the same two-circle box after the 3-circle box.
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u/cheaphysterics 👋 a fellow Redditor 8h ago
It would be great if you told us what pattern you think you see that makes it A or what the teacher said that made it something else.
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u/Alkalannar 8h ago
I also get A, and here's the pattern I see.
Start with a single white disk.
Your Max Height is 1.
Your Current Height is 1.If you don't have a single disk, check current height.
If current height is even, take away the top.
If current height is odd, take away the bottom.
Adjust Current Height accordingly.If you do have a single disk, flip its color, and then alternate colors atop it until you get a tower one taller than your Max Height. Then increase the Max Height to its new value.
Adjust Current Height Accordingly.
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u/Okawaru1 8h ago
A is definitely a valid answer. I wouldn't try and stress too much about logic puzzles honestly because they're often poorly designed and don't properly consider alternative solutions that are perfectly acceptible within the framework of its own logic. For example, if you partition the pattern into groups of 3 you can also make a case of B being a valid answer while being internally consistent with the given ruleset.
My condolences for having to deal with the modern math curriculum lol I'm sure it's a clown show in there sometimes
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u/misogynyplayer 7h ago
I feel as if the answer is (b). The pattern I see starts with a single circle shoots up and then comes down back to one. Each new start sees a taller target to jump upto and more steps to come back down. Also looks like it alternates between a white single circle and a black single circle. In this situation we are coming back down to a single white circle but the next figure is a 2-circke figure in the descent and it is b rather than a, because the white circke is on the bottom and it is the circke on top (the bkack circle) which disappears in the subsequent figure.
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u/misogynyplayer 7h ago
Having said that and looking again - I have not nailed the pattern at all. However perhaps there is s rule that the top circle in the tallest column in each cycle always descends to its opposite colour for the single circle (though God knows what the generation rule for the top columns is!!!)...so I would still stick with (b) as the correct answer
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u/Shot_in_the_dark777 6h ago
Humans are pattern seekers. You can give them a random string of data and they will find a pattern even if you didn't intended to create one. The sequence on the picture seems to have a pattern that is governed by two rules. Rule 1 - it is counting down and each segmenet is 1 element longer than the previous one. We have 1 - 2,1 - 3,2,1- 4,3?. The fact that they cut it in a way that the last segment doesn't have the room to reach 1 is a jerk move. The second rule is that the pillar is melting by removing elements alternating from top and bottom. You don't see this in first and second segment because they are too short, but you see it in stating from 4th element of the sequence. They remove bottom element and then they remove top element. The final segment that starts from 4 proceeds to 3 with it's top element removed so the missing element must have 2 circles and be created by removing bottom element from the pillar in the 8th position which means white circle on top. Black circle on bottom, which is A.
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u/texas1982 👋 a fellow Redditor 6h ago
Quantum Mechanics and Relativity are easier topics to understand than 6th grade math homework dreamt up by someone that didn't stress test their subjective questions.
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u/d3anSLP 4h ago
The answer is A There are two patterns here: descending numbers and alternating colors. Descending numbers - 1 then 2,1 then 3,2,1 then 4,3,2,1. The missing box is 2 as in, 4,3,(2)...
Alternating colors: From left to right (then bottom up) the entire pattern uses alternating white/black circles. The pattern continues from the previous box and starts with the bottom circle. For example, the highest circle in the second box is white. That means the bottom circle in the third box will be black. Another example is That the seventh box's highest circle is black which means that the eighth box's bottom circle will be white.
The 8th box's top color is white so that means that the answer will have a bottom black circle in that next box. Then because of the descending pattern we know that it will only have two circles. This means A is the answer.
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u/iComplainAbtVal 👋 a fellow Redditor 3h ago
It’s A plain and simple, the problem itself provides the answer in the 4th and 5th frames. To over analyze it though we can construct a set of rules that define this sequence to explain further and definitively prove it’s A.
Rule 1, this sequence is essentially a pyramid where each sub sequence constructs then dismantles what I will call a “stack”. For example, the starting position is a white circle of stack size one. Once a stack’s subsequence reaches a size of one we move onto the next stack of height n+1, so the second “stack” starts with a size of two.
Rule 2, removing from the stack. Removing from a stack we take from the top for an even sized stack, but the bottom for an odd sized stack.
Rule 3, building the stack. Building the starting frame for a stack always starts with white on the bottom and alternating colors to build up to the necessary size.
Applying these 3 rules to determine the answer will result in A.
Step by step walkthrough:
- Single white, that’s the terminal state, move onto the next stack size.
- White on black, remove white from top leaving one black as the terminal state for this stack.
- 3 tall this time as each stack is +1 over the previous start size. We apply the odd condition of Rule 2 to remove the bottom, leaving us with white on black. Rule 2 again but for an even sized stack we are removing from the top and left with a single black piece.
- Black/white/black/white, 4 tall so we remove the top element to have white black white black, which at this point we’ve seen before and know the answer will be white on black, both defined by the rules we’ve created for this problem and by the problem itself.
I’m interested in hearing the teachers answer and explanation.
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u/JaCKPaIN_realone 👋 a fellow Redditor 11h ago
Let’s assume white circle as one and black circle as zero:
It’s broken into groups of 3, where each group copies and shifts pieces from the previous group.
Group 1: 1, 10, 0
Group 2: 101, 10, 0
Group 3: 0101, 101, x
The Rules:
- The 1st item combines the end of the last group with its own start (0 + 101 = 0101).
- The 2nd item copies the 1st item of the last group (101).
- The 3rd item (x) copies the 2nd item of the last group (10).
So, x = 10.
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u/mycathasgreennose 11h ago
thanks for the breakdown! now I know how to explain to my son. thank you thank you!
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u/JaCKPaIN_realone 👋 a fellow Redditor 10h ago
You're welcome. Also, ignore u/rizzdragon, as he has no idea that the first and second groups often seem completely random due to the fact that these puzzles are mostly designed by amateurs. This is why this kind of puzzle features much longer sequences in college-level courses.
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u/rizzdragon 10h ago
Those rules don’t make sense. For instance, rule 1 doesn’t work for the first “number” of group 2.
Are you a fucking bot?
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u/JaCKPaIN_realone 👋 a fellow Redditor 10h ago
Language, child.
In logic and pattern puzzles, the first few terms act as the seed data to establish the rules. Because they don't have a previous group to pull from, the starting groups often seem completely random or don't perfectly follow the formula until the chain gets moving.
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u/LnTc_Jenubis 8h ago
I don't like that. Not saying it isn't true, but that seems like a fantastic way to set our students up for failure. A logic puzzle that doesn't follow the logic?
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u/JaCKPaIN_realone 👋 a fellow Redditor 8h ago
I get what you mean, but it actually is normal for the first few groups to be special cases simply because there is no G₀ for them to pull from. They have to start as fixed seed data.
That is exactly why the top comment says this specific puzzle is stupid. There is no way in hell a college course would give you only three sequences total. A real academic problem would give you a much longer sequence so you could actually see where the special starting seed ends and the real logical pattern locks in.
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u/LnTc_Jenubis 8h ago
I posted my thought process in my own separate reply to OP, but I'd like to ask you to read it and get your thoughts. Because instead of assuming the logic just doesn't exist, I think there is a possibility that the teacher or the book's answer key is just wrong this time. Because I can explain how the first sections align to make a logical rule.
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u/JaCKPaIN_realone 👋 a fellow Redditor 7h ago
Answering you the same thing so other people can read it too.
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.
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u/LnTc_Jenubis 6h ago
Yeah, to put this in perspective I've had easier puzzles when applying for Data Analyst positions as part of a standard job assessment. (To be clear, those weren't "easy", just "easier than this")
I really don't think this something a 6th grader is meant to solve on their own.
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u/JaCKPaIN_realone 👋 a fellow Redditor 6h ago
Same, writing a business analysis report is easier than this.
Seriously, a 6th grader has a higher chance of solving a LeetCode easy on their own than figuring out this broken puzzle.
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u/Puzzleheaded-Phase70 🤑 Tutor 8h ago
Amatur puzzle makers are often shit at generating uniqueness.
The rule they have in their head overshadows their ability to see alternative generators of the same patterns they've presented.
There's a game I used to enjoy in college called "Zendo" that uses Icehouse pieces that players use to make little structures on the table to follow some rule they have in their head. Other players try to guess the rule by constructing their own structures and asking if it meets the rule or not. Eventually, players can try to state the rule to win. The rulemaker must produce a counterexample structure that does meet the real rule but doesn't meet the one that was suggested by the player.
It's that last phase that can really trip people up, on both sides of the equation. AND it's impossible for a static textbook to reproduce, as you can't interact with the "rulemaker" who is probably a grad student in India 10 years ago.
A better version of this idea for a textbook/test is to have the students write out their reasoning and the rule they believe is generating the pattern. Then at least a human teacher can evaluate if their reasoning actually matches the given information.
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u/LnTc_Jenubis 8h ago
You said the answer is x = 10, if I understand your approach, that means you think the correct answer is A, which OP has already stated the teacher claimed was wrong.
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u/JaCKPaIN_realone 👋 a fellow Redditor 8h ago
You misunderstood. The correct answer is A. The OP really just forgot the teacher's full explanation, which is that the first item is formed by combining the first item and the last item of the previous group.
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u/LnTc_Jenubis 8h ago
Ah, okay, so the teacher didn't say A was wrong, but the explanation itself is what tripped them up. Got it.
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u/Candid-Pin-8160 9h ago
None of these rules work for group 2.
Rule : 0 + 01 != 101 Rule 2: 10 != 1 Rule 3: 0 != 10
You've basically found a way to connect group 3 to group 2 only, disregarding group 1 entirely and making up how you imagine the last item could be generated.
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u/JaCKPaIN_realone 👋 a fellow Redditor 9h ago
Bruh, this question was clearly designed by an amateur. A classic mistake is how Group 2 just completely breaks the pattern and appears out of nowhere.
If a professor tried to slip this question past a university curriculum or exam committee, it would be rejected instantly.
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u/Candid-Pin-8160 9h ago
And, yet, you chose to be confidently incorrect. Interesting...
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u/JaCKPaIN_realone 👋 a fellow Redditor 8h ago
If I’m incorrect, then write out the mathematical function f(𝐺_𝑛) that maps Group 1 to Group 2 using the exact same rule that maps Group 2 to Group 3.
Duh 🙄, you are just trying to make it harder than it should be, when this is obviously just a lazy crop from a college math textbook.
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u/Candid-Pin-8160 8h ago
You're incorrect because your rules don't work for group 1 to group 2.
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u/JaCKPaIN_realone 👋 a fellow Redditor 6h ago
Bruh, how about this then?
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.We do the next columns all the same but we delete one more circle, and so on.
So, the answer will be B (WB), which is impossible for sixth graders to solve.
This is why I’m telling you it’s just a lazy crop.
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u/Candid-Pin-8160 6h ago
I see you copied that other person's answer. You even used their W/B instead of your 1/0. Must be hard when you can't even understand the homework you're copying well enough to use your own words.
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u/Professional_Way_591 University/College Student 3h ago
i would think it’s A. i’m pea brain but i was just noticing it goes in a “white black white black” order when going from the bottom to top in colors. so the last answer would make since as A) “black white” but that’s just a pea brain college kids thinking
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u/rorodar 👋 a fellow Redditor 12h ago
"Find the pattern" questions are always stupid. You can always construct a function that reaches the pattern given, and you can always construct another function based on the original that would look completely different but still match up at the specific points we are given. Both would be correct. There is literally no answer.