Hello Community,
I had a math learner ask me to figure out this pattern and it has got me stumped - so I am looking to you all for a solution:
| 6 | 6 |
| 3 | 8 |
| 9 | 12 |
| 7 | 8 |
Then using the following numbers pick the correct input and output: 36, 7, 8, 9, 12
Any thoughts?
Brooke
Comments
Brooke,
This is intriguing, but doesn't feel like enough information to me. This is supposed to be an in/out table, right? And could be reorganized like this?
In Out 3 8 6 6 7 8 9 12So, the task is to fill in the following numbers as input or outputs in this table, right?
36, 7, 8, 9, 12
If the only outputs for sequential inputs are 6 & 8, I don't know how we could see a pattern with these numbers.
Was your student sharing this from memory?
- Eric
I coudl imagine guessing combinations of operations -- it's not linear.... so I am sure that, given enough time, I could invent some combination of things to do...
... but mainly I am having a flashback to a problem presented here where the so-called answer was actually, mathematically wrong... based on the actual "problem" as given, a "correct" input and output would be7 (in), 8 (out), 9 (in), 12 (out) because we were told that was what happened. The 36? That's not on the list so I'd leave it out. There are an odd number of numbers there so they dont' match.
To start, your student will want to re-arrange your values in your first column in sequential order to find the formula.
3, 8
6, 6
7, 8
9, 12
n + ( | n-7 | + 1 ) works for all but the 6,6
It would be very convenient if the learner simply made the mistake of transposing 3,0 into 3,8 for that number combination. Is that possible?
If this is the case that there was a transposition error, the following input and output would be generated with the other numbers you offered:
36, 30
7, 8
8, 10
9, 12
11, 16
That seams strange because they were already given information about 7 and 9 in the chart. Seems there is something unclear or incorrect with the data set provided. Can you verify the table is accurate?
Ed,
Yes, I will verify that the learner gave me the correct problem - and let you know.
Thanks,
Brooke
Okay the values are 3,6,7,8,9,12...and the learner said that you can't use the same value that was already an input value. I am not sure there is a solution.
The equation y=|2x-10|+4 works for the given set. :)
I'm not sure what you mean to do with the 36, 7, 8, 9, 12 (?).
I found the same solution as above by shepar... but I found it easier to see when expressed in the form y = 2*|x-5| + 4 . Namely, looking at inputs 6, 7, 9 it is clear that we could insert input 8 and output 10 so that part is linear with an increase of 2 each time. Working back gives input 5 and output 4. And then by symmetry around 5 we see that to the left of 5 we could have a linear output with a decrease of 2 each time to give (4,6) and (3,8) and ...
Thanks for the clues :) I was going through "what operations go up and back down" logic and too busy/lazy to graph the points... and for the student in question it was probably in the context of learning about absolute values.
Those are the values that a learner was given to place one of those as an input and one of them as an output.
Was the question "Which numbers could be added to the table to show a function?"