Help Explain Correct Answer to my Friend .....

[GadgetJim57]

*** I work part-time as a substitute teacher, all grades, all subjects. I like to share fun Math, like Math Puzzles, with students when the opportunity arises. I found some really cool Math Puzzles which I shared with a good friend, but he disagrees with me regarding the correct answers. I know how to get the correct answer to this Math Puzzle, but I could use some assistance with trying to explain to my good friend where he is mistaken. Here is my friend's response to me:

***
It could be this...
6 x 9 = 54
5 x 8 = 40
4 x 7 = 28
3 x Y = Z
2 x 5 = 10
-- But then the answer would NOT be following the GIVEN PATTERN and this puzzle would become like a woman who is not being direct.
-- 1) this puzzle IS NOT ASKING you to fill in a missing grid, SO THAT CANNOT BE ALLOWED! PERIOD!
-- 2) This puzzle IS asking you to find a pattern WITH AND ONLY WITH THE EXISTING information, not by adding to it.
-- 3) inserting something into this would be adding to the MATH PUZZLE WHICH CANNOT BE ALLOWED BECAUSE THAT IS NOT the scientific way and that derails away from EXACTLY what the equation is asking. (It is ONLY asking for the next number, nothing more and nothing in between!)
-- 4) the scientific way is to answer only the question in which you are asked.
-- 5) if the puzzle wanted another grid row, then it should've been written EXACTLY LIKE THIS: ("make this pattern complete by inserting steps in order to discover the missing "??"
-- 6) if the puzzle didn't read those exact words VERBATIM, then it is a puzzle WRITTEN BY A PRESCHOOLER WHO ADDS THE RULES AS THEY GO ALONG. SIMPLE AS THAT.

Don't tell me they wanted you to add an extra row. Cuz THAT'S NOT AT ALL what they asked for!
========================
*** So, what I see here is that Mike Sawyer is right, and everyone else is wrong ! Are you even willing to entertain the thought … possibility …. that you could be mistaken … ??? (My personal note: Wednesday, July 8th, 2020, @ 1:37 p.m.)
*** Math Puzzles: I found this math puzzle. I know how to get the correct answer, but I need help to explain respectfully to a friend how to get the correct answer. This is what they wrote for their answer .....
It could be this...
6 x 9 = 54
5 x 8 = 40
4 x 7 = 28
3 x Y = Z
2 x 5 = 10
-- But then the answer would NOT be following the GIVEN PATTERN and this puzzle would become like a woman who is not being direct.
-- 1) this puzzle IS NOT ASKING you to fill in a missing grid, SO THAT CANNOT BE ALLOWED! PERIOD!
-- 2) This puzzle IS asking you to find a pattern WITH AND ONLY WITH THE EXISTING information, not by adding to it.
-- 3) inserting something into this would be adding to the MATH PUZZLE WHICH CANNOT BE ALLOWED BECAUSE THAT IS NOT the scientific way and that derails away from EXACTLY what the equation is asking. (It is ONLY asking for the next number, nothing more and nothing in between!)
-- 4) the scientific way is to answer only the question in which you are asked.
-- 5) if the puzzle wanted another grid row, then it should've been written EXACTLY LIKE THIS: ("make this pattern complete by inserting steps in order to discover the missing "??"
-- 6) if the puzzle didn't read those exact words VERBATIM, then it is a puzzle WRITTEN BY A PRESCHOOLER WHO ADDS THE RULES AS THEY GO ALONG. SIMPLE AS THAT.

Don't tell me they wanted you to add an extra row. Cuz THAT'S NOT AT ALL what they asked for!
=========================

[fiveworlds]

 

It looks to be

Or approximately 2??

[Dord]

10

[Strange]

 

11 hours ago, GadgetJim57 said:

I know how to get the correct answer to this Math Puzzle

Odd that you don't tell us what you think the answer is, then.

As with all these stupid puzzles, I guess one can make up a story to justify any answer, but in this case it seems reasonable to say (as your friend's list shows) that the answer is N * (N + 3) = 10.

I don't understand what all the shouting about (or what your friend said vs what you said) or why you have posted everything twice. Is that part of the puzzle 🙂 

[MigL]

There is enough information in just the second column to arrive at an answer.

One trick I learned almost 45 years ago ( from a 'tough as nails' high school algebra teacher ) to find patterns in a number sequence, is first , second, and sometimes even third differences. The differences between 54, 40, and 28 are 14 and 12, but the second difference is constant at 2.
The pattern would continue with 1st differences of 10 , 8, 6 and 4 ( this is equivalent to the example you give with the X and Y unknowns ).

That is usually the irst thing I try when dealing with number patterns. 

[GadgetJim57]

On 7/9/2020 at 1:22 AM, Strange said:

 

Odd that you don't tell us what you think the answer is, then.

As with all these stupid puzzles, I guess one can make up a story to justify any answer, but in this case it seems reasonable to say (as your friend's list shows) that the answer is N * (N + 3) = 10.

I don't understand what all the shouting about (or what your friend said vs what you said) or why you have posted everything twice. Is that part of the puzzle 🙂 

I already knew the correct answer is 10. The sequence is quite obvious to me, but my friend disagrees, as you can see from his response. He is very stubborn.

On 7/8/2020 at 3:14 PM, fiveworlds said:

 

It looks to be

Or approximately 2??

Thanks for taking your time to solve this Math Puzzle algebraically ... !!! I'm not very good with Algebra. I'm ok with basic Math. I shared this Mathematical Proof with my friend and others. 

On 7/9/2020 at 1:22 AM, Strange said:

 

Odd that you don't tell us what you think the answer is, then.

As with all these stupid puzzles, I guess one can make up a story to justify any answer, but in this case it seems reasonable to say (as your friend's list shows) that the answer is N * (N + 3) = 10.

I don't understand what all the shouting about (or what your friend said vs what you said) or why you have posted everything twice. Is that part of the puzzle 🙂 

Long story ..... I'm concerned that my friend has some issues .... I won't go into the details here. But I do believe that his thinking is distorted .... He is extremely (to the MAX !!!) skeptical about everything and everybody ... That might give you a clue to his problem. All I did was simply share the Math Puzzle. I did not add anything. I just sent him the image of the Math Puzzle. He then went ballistic when he gave me his answer, and I simply told him try again !!!

[HallsofIvy]

I would say that the answer is clearly "10".  As far as an explanation is concerned my first thought would be to note that  the numbers in the left column are decreasing by "1" each time, that 54 is 9 times 6, that 40 is 8 times 5, and that 28 is 7 times 4 so following that pattern, the "next row" would have 3 on the left, and 6 times  3= 18 but that row is missing so the next row has "2" on the left and then 2 times 5= 10.

But you don't like that explanation because, for some reason, you don't like the appeal to a "missing row",  So, instead, I would say that each number on the  left is decreasing by "`1" until we get to the last, "2", which is 2 less than 4.   I would also note that each number on the right is the number on the left multiplied by 9, 8, 7, also decreasing by 1.  but since for the last step the left number decreased by 2, I would also decrease the multiplier by 2 to 7- 2= 5 and so the number on the right is 2*5= 10.

 

That is the same explanation but without appealing to  a "missing row".