Question 1199253: The positive integers greater than 3 are arranged in rows and columns as illustrated. In which column is the number 5018?
https://ibb.co/G5y6tR3
There is a solution by math_helper here:
https://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.1171707.html
But it is literally just a procedure on how to solve and makes ABSOLUTE NO SENSE TO ME OR ANY STUDENT WHO NEEDS TO 'SHOW [THEIR] WORK'.
Can someone please explain how and why this solution works, and what it is even achieving with the modulos 12?
Thanks.
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Mod 12 was used because the gap from 4 to 16 is +12 (when going from row1,column1 to row3,column1). Or put another way: each row has 6 items, so two such rows have 2*6 = 12 items.
The left/right pattern repeats every 12 items.
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I'll take another approach.
Notice the third column has 6, 14, 18, 26, ...
We can extend that a bit to say: 6, 14, 18, 26, 30, ...
The 30 is from writing the next two values in row 5.
Now focus on the odd numbered terms of that sequence.
Those terms are 6, 18, 30, ...
All of which are multiples of 6.
Specifically they are odd multiples of 6.
An odd multiple of 6 is of the form 6n, where n is some positive odd integer.
6*1 = 6
6*3 = 18
6*5 = 30
and so on.
Another thing to notice is that the rows involving 6,18,30,... all have the terms in increasing order from left to right.
This corresponds to odd numbered rows.
Let's divide 5018 over 6
5018/6 = 836.333 approximately
Rounding up to the nearest odd number gets us 837
Then,
6*837 = 5022
This value is in column 3 to keep up with the pattern mentioned above. This item is in row 837.
The value 5022 is 4 units over the target of 5018.
So we have to go to the left 4 units.
Going 2 of those units to the left gets us from column 3 to column 1.
Then we'll bump up to row 836, which will move us to column 2 in the process.
This is the third step out of 4 total.
The fourth final step gets us to column 3.
Here's a mini table showing what's going on
| Column 1 | Column 2 | Column 3 | Column 4 | Column 5 | Column 6 | Column 7 | | Row 836 | | 5019 | 5018 | 5017 | 5016 | 5015 | 5014 | | Row 837 | 5020 | 5021 | 5022 | 5023 | 5024 | 5025 | |
One thing I forgot to mention is that each even numbered row goes in reverse, so we'll use that fact to count down from 5019 to 5018.
Answer: Column 3
Answer by ikleyn(52798)  (Show Source):
You can put this solution on YOUR website! .
I like the solution by tutor @math_helper very much
and do not understand why you are so much against it.
In my view, it is a PERFECT solution,
and I do not understand why you do refer to ANY student.
If you do not understand that solution,
you may refer on yourself, ONLY - why do you refer to ANY student ?
That solution works, because the remainders of dividing by 12
repeat with no change from one pair of lines to the next pair of lines.
and, therefore, from the very first pair of lines to any other pair of lines.
Absolutely perfect, short, clear solution without excessive words.
True Math solution.
It would be much more appropriate if you express many thanks to tutor @math_helper
for his bright idea, which he shared with you generously, and for his brilliant work . . .
" Any student " may sleep peacefully - he has nothing to do with your reference.
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