Math Puzzle .....

[GadgetJim57]

*** 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!

 

[HallsofIvy]

You talk about "solving a problem" but you haven't said what the problem is!

You show a chart which has two columns of number, the bottom has the right side column with ??? instead of a number and then it says "Solve This". Solve what? No problem has been explicitly stated!

If I were given a "puzzle" like this, the first thing I would have to "solve" is "What question are they asking?" And, observing that one square has "???" where all the others have numbers, I think it would be perfectly reasonable to conclude that they want you to replace "???" with a number. And that requires "guessing" the rule or pattern being used.

When I was in college a mathematics professor gave the class the sequence 131, 130, 129, 128 and challenged the class to determine the "next number" in the sequence. Of course, every one said "127" at which point the professor responded, "No, the next number is 87"! What? Had the man gone mad?

No, the sequence consisted of the exit numbers on his drive to work each morning. He took exit 128 onto a different highway which had different exit numbers.

His point was that a "sequence" can consist of any numbers in any possible order. Typically, problems like this have the "hidden requirement" that you are to find the simplest pattern out of many possible patterns.

Seeing a problem like this and thinking "simplest pattern", I would observe that 54 is 6 times 9, 40 is 5 times 8, and 28 is 4 times 7. The next number on the left is "2" so I would thin "2 times 6 equals 12" since 6 is next number in the sequence 9, 8, 7. I would think that the correct answer to the puzzle is to replace the ??? with "12".

You say, vehemently, "Don't tell me they wanted you to add an extra row. Cuz THAT'S NOT AT ALL what they asked for!". So what do you think they are asking for? I think they are asking us to replace "???" with the number that follows the simplest pattern- and, in my opinion, that is "12".

If you are complaining about your friends adding the row "3 X Y = Z", I would say, yes, that was not asked. But I don't understand why you are so exercised over this. It might be that they thought that would help. I would say that, "No, that will lead you astray" since then you might be led to say "3x 5= 18" and then "2 x 5= 10", replacing the "???" with "10" rather than 12. But, as I said, problems like this involve "guessing" a pattern. They have come up with a different pattern. I would argue that it was not, in my opinion, the "simplest" pattern but they might disagree. In the end, puzzles like this require "guessing" what was in the mind of the person who created the puzzle!

 

[Dr.Peterson]

Since the first column is not an arithmetic sequence, the puzzle is not about sequences. It is about functions.

Filling in a missing row can, however, make the pattern of the function easier to see. When the input decreases by 1, so does the number you have to multiply by. This fact generalizes to something that does not depend on filling in that row: the output for input x is x(x+3):

6(6+3) = 6(9) = 54​

5(5+3) = 5(8) = 40​

4(4+3) = 4(7) = 28​

so

2(2+3) = 2(5) = 10​

None of your complaints apply.

On the other hand, it is entirely true that this is a riddle, not a math problem, because the problem is not well-defined. The answer is not unique, and any answer you can justify can be considered valid.

 

[Cubist]

I prefer a function that has a cube in it, like (x^3 + 119*x)/15 - 8, therefore the missing number is obviously 8.4

 

[Steven G]

I think that you refusing to acknowledge the missing row is silly.

What if you had the following.

1 2
2 4
3 6
5 ???

Surely you see the that you double the number in the 1st row to get the number in the 2nd row. But wait that skipped 4 so there is no answer? Are you serious?

 

[Steven G]

I prefer a function that has a cube in it, like (x^3 + 119*x)/15 - 8, therefore the missing number is obviously 8.4

Cubist prefers a cube. Who would have guessed!