"Banana clock shapes" puzzle on social media

[BernieM]

I looked for an answer to this question other places but found none. There is a puzzle going around that people are getting the answer wrong to. No surprise there. According to the proofs I found for it on the internet, my assumptions were true and I did arrive at the right answer (38 apparently, but I feel it is actually just one of many possible answers as I had to make assumptions.)

I have a disagreement with another that there is more than one possible right answer to the problem, so there is technically no 'right' answer that can be deduced solely from the puzzle itself and what is contained there. Here it is:

https://mindyourdecisions.com/blog/2017/03/09/the-bananas-clock-hexagon-viral-logic-puzzle/

Now my assertion is not that 38 is right or wrong, but that there are alternative solutions to the puzzle, which satisfy all information given in the puzzle problem. I assert that without making assumptions, there is no absolute right answer to the problem. What is the proof of this or am I mistaken?

One example would be say that the hexagon has a value of 7, the pentagon 5 and the square 3 which is equal to 15 satisfying the 1st line in the picture. I see nothing anywhere that says that the value should be equal to the sum of the sides in a shape. It's an assumption. (The actual deduction given in the proof was that each line segment has a value of 1) Calculated using one assumption, that each line segment is equal to one, then the bottom shape has a value of 11, and the other way it is 12. Hence there can be no true solution. I'm sure alternatives probably exist for the banana and clock as well.

So, the question is, simply:

Without more information, is it actually possible to prove that there is only one right answer to this problem, using logic, mathematical proofs, etc.

 

[Baluncore]

The 12 hour clocks have two identical hands, should the angle between the hands be measured, giving 2, 3, 9 or 10. The time is; 0300, 1500; 0015, 1215, 0200, 1400, 0010 or 1210. Should those be converted to decimal hours, whole minutes or to longitude of the Sun in degrees?

Should you count the lines, all the areas in, or only the triangular areas in the polygons that show squares and above? Is the outside also an area?

The number of lines used to draw the bunches of 3 or 4 bananas is 4 or 5.

Do the two identical ?? mean a multiple of 11. Must it be written in base 10, or can the problem be solved in any base greater than 6? Must we find the number base that gives a result in the integer, n, form of n*base + n. Could the answer then simply be the base needed to make it work?

I can see many possible solutions. There can be no one correct solution. It is roulette, a game of chance.

 

[BernieM]

Thanks admin for changing the post to the correct rating (Advanced, Intermediate, etc.) as I didn't know where to place it.

Baluncore, I agree. I hadn't considered the base, that's an interesting angle. There are 10 kinds of people in the world, those that understand binary and those that don't.

But even if it's only base 10, using single, simple rules, one can come up with alternatives. Though the Hexagon-Pentagon-Square is equal to 15 by the example given in the problem, the Hexagon-Pentagon must be considered a different identity with no connection to the Hexagon-Pentagon-Square even though they look similar. For example, Z +z = 4 does not prove that Z and z are both equal to 2 even though they look 'similar.' Or that Z=3 and z=1 because they are similar but not the same in appearance. Z+z is functionally equivalent to Z + y Z+X or any other variable. An entirely different identity, not proven to be related to the first by anything other than a physical appearance.

 

[BernieM]

The 12 hour clocks have two identical hands, should the angle between the hands be measured, giving 2, 3, 9 or 10. The time is; 0300, 1500; 0015, 1215, 0200, 1400, 0010 or 1210. Should those be converted to decimal hours, whole minutes or to longitude of the Sun in degrees?

Should you count the lines, all the areas in, or only the triangular areas in the polygons that show squares and above? Is the outside also an area?

The number of lines used to draw the bunches of 3 or 4 bananas is 4 or 5.

Do the two identical ?? mean a multiple of 11. Must it be written in base 10, or can the problem be solved in any base greater than 6? Must we find the number base that gives a result in the integer, n, form of n*base + n. Could the answer then simply be the base needed to make it work?

I can see many possible solutions. There can be no one correct solution. It is roulette, a game of chance.

The problem I see in the math puzzle is that it requires speculation as to the values of the different variables in the last line, which are not seen before in the puzzle. If one replaces the different symbols with variables, it becomes very clear that the problem is not solvable:

A+A+A = 45 A=15
B+B+A = 23 23-A = 8 2B=8 B=4
B+C+C = 10 10-4=6 2C=6 C=3

Final line:
D+E+ExF = ??

So to arrive at an answer requires speculation as to the meaning of the appearances of the symbols, for which multiple possibilities exist, as you have mentioned and as I have mentioned. But what is the mathematical proof of it? That there can be either multiple 'correct' answers or that there is no one correct answer? How would one go about proving it mathematically? Would one use set theory? Algebraic proofs? Logic proofs? Combination of these? What would it look like? Because clearly either as a mathematical problem, either things like the number of sides of a shape, color, etc., are relevant and provably part of the mathematical requirements to prove the solution or they are irrelevant and can not be taken into account in the problem.

In short, if there is no ONE right answer to the problem how can that be proven mathematically, or is it too complex to prove.

 

[Charles Kottler]

A+A+A = 45 A=15
B+B+A = 23 23-A = 8 2B=8 B=4
B+C+C = 10 10-4=6 2C=6 C=3

...The hands in the clocks in the first line of clocks point to 3 O'clock and have a calculated value of 3 so it seems reasonable to me to assume that the clock on the last line has a value of 2. Then just apply the normal rules of precedence...

 

[DrClaude]

The problem I see in the math puzzle is that it requires speculation as to the values of the different variables in the last line, which are not seen before in the puzzle.

Exactly. If they were other equations, such that one could infer, .e.g, that a bunch of bananas with two bananas is worth 2, then one could make valid logical inferences concerning the last equation, even if the particular symbols were not previously seen.

I would argue that, as the problem is posed, 67 is an equally valid solution (based on the fact that a bunch a bananas is worth 4, however many bananas there are in it, etc.).

 

[BernieM]

...The hands in the clocks in the first line of clocks point to 3 O'clock and have a calculated value of 3 so it seems reasonable to me to assume that the clock on the last line has a value of 2. Then just apply the normal rules of precedence...

True. But it is an assumption. Supposing you are right in the case of the 2 being the value because the hand points at it. And that the bananas have a value based on the number of bananas in the bunch. Both assumptions that appear to be true. But as well, the designer of the puzzle could have also just accidentally or subconsciously used those symbols for the actual value they just picked out of the air for those to have. There is no information in the puzzle as to how the values were arrived at by the designer of the puzzle. So we are forced to make assumptions. Use logic I guess. So now that there is a connection to the clocks and bananas and their respective values, does this logically carry over to the shapes? The wisdom of the crowd so to speak says it does, that the # of lines = the value of each shape. But for that matter, it could be the number of angles, as there are also the same number of those in each figure as line segments. As well, one could make a number line and take the first 2d closed regular shape (triangle) and put it above 1 on the number line, then each additional side added creating a new shape, a square would be above the 3, a pentagon above the 5, the hexagon above the 7, etc. And in this manner there is an actual other simple method that shows how the values were calculated for each shape that adds up to 15 in the first rows, but in the final row, comes out as 12 instead of 11, providing another possible right answer, that could be fairly reasonably proven to be a possibility as to the values of the shapes.

The belief that what applied to the clocks or bananas can be extended to the shapes is not logically provable, though possible, as I see it. It's like saying that if A=5 and a=4, and B=7 and b=6 then what are the values for C & c ? It appears that C must be >c and the values for C = 9 and c = 8 based on the previous examples. As it follows some pattern that seems to be established by the first two cases. But there is no proof (or requirement stated in the puzzle if it were that) that a pattern is required or actually exists. That it could simply be coincidental.

Basically it calls for the individual to assume things not in evidence as true. And I don't know how that can be expressed in a mathematical proof. So C could be any number as well as c, and c could be < C as well as > C. No way to know or prove it as I see it. The same problem that exists in solving the puzzle.

Exactly. If they were other equations, such that one could infer, .e.g, that a bunch of bananas with two bananas is worth 2, then one could make valid logical inferences concerning the last equation, even if the particular symbols were not previously seen.

I would argue that, as the problem is posed, 67 is an equally valid solution (based on the fact that a bunch a bananas is worth 4, however many bananas there are in it, etc.).

True, 67 works. All one has to do is go by the color (all yellow symbols = 4, all white symbols 3, and all gray symbols 15.) So quantities of elements in the symbol thus become irrelevant.

But how could one state mathematically, a proof, of one of the following most true cases about this puzzle?

A) that either there is only one correct answer
B) that there is no possible correct answer (insufficient information to determine the last row's values)
C) that there are multiple possible correct answers

... based solely on the puzzle as it appears, and the information provided therein?

I would think that if one were to engage more than just arithmetic or algebra, and the established values found in the puzzle, using perhaps inductive and deductive logic, that one would have to establish the logical principles and proofs, no? In other words prove the logic first that allows one to deduce an actual value, that the deductions are valid and provable, which then yields one or more options for the unknown values in the last row.

 

[BernieM]

Even the statement that "99 percent fail to find the correct answer." Implies logically that there are not multiple answers to it, that there is in fact only one right answer. And since it can be shown that there are multiple possible ways to interpret (provably) the values for the final row of variables, that yields multiple answers, that the puzzle is impossible to solve due to the fact that one of the two is a lie: I.e., that either there is not only one possible answer, or that there are multiple possible answers, which are contradictory. Think I am on the right track? I take the statement regarding the puzzle as information regarding it as well. Is that wrong? Further, this contradiction is further highlighted below the puzzle where it says 'Can you figure it out? Watch the video for a solution.' which means that there is more than one solution (a solution.) So even in the words above and below the puzzle the contradiction exists and seems to prove that there is no one correct answer, at the very least.

 

[DrClaude]

But how could one state mathematically, a proof, of one of the following most true cases about this puzzle?

A) that either there is only one correct answer
B) that there is no possible correct answer (insufficient information to determine the last row's values)
C) that there are multiple possible correct answers

... based solely on the puzzle as it appears, and the information provided therein?

Mathematically, the problem is ill posed.

Even the statement that "99 percent fail to find the correct answer." Implies logically that there are not multiple answers to it, that there is in fact only one right answer.

If that number was not pulled out of a hat, I'll eat mine

 

[BernieM]

Mathematically, the problem is ill posed.

If that number was not pulled out of a hat, I'll eat mine

I agree 100.00000000000000000001% <---- floating point error.

OK well let me give a stab at this and see how I do:

There are two parts of the 'puzzle'. The first part is attempting to identify common factors between the values in the bottom row with those in the top row and making the assumption that there is a correct answer that can be had. Though the majority of people have chosen to identify a number somehow associated with each of the symbols in the bottom row, the method used for each differs. Example, Bananas either 4 or 3 depending on counting what one assumes are representations of a banana. IN the upper portion of the puzzle there appear to be 4 in the bunch, below, 3. With the clock it is not the summing of items but the actual number that one of the hands on the clock points to, the only one that changes position between the upper and lower one. So in the upper portion, 3 and in the lower case, 2 is the value for the clock. And with the shapes, one can either count the number of lines or the number of points (angles/junctions between line segments) and a value of 15 is arrived at for the upper portion, a value of 11 in the lower portion. So to arrive at these values requires 3 different rules or 'assumptions' to establish the values for all 3 symbols (variables.)

But in all three of these cases, a different rule had to be applied. In one case it was the number of bananas, the clock, an actual number being pointed at, and the shapes the number of lines required to construct the symbols. There is no one universal rule used in all 3 cases, and there are other options as well. Other values that can be arbitrarily assigned or assumed, etc. But this would defeat any value of being a puzzle that could be proven solvable (as it is assumed that there is only one solution.)

But there is a single, universal rule that is apparent across all three symbols. The color (not considering the outline color, black.) The bananas in the upper portion and lower portion are both yellow, the clock in both cases is white and the shapes are gray. So from this we should prefer this as the preferred method for valuation of the symbols, because it is a single rule that's universally applicable to all symbols. So any yellow symbol = 4, any white symbol, 3 and any gray symbol 15, the values for which each has been established in the upper portion of the puzzle. So all the values of the last line are known, and using one single rule instead of 3 different rules to determine the values is preferred. Occams razor states that the simplest solution is always the better solution. So without any evidence contradicting this in the puzzle, this is the best and only truly provable solution to the problem.

This results in a value of 67 in the final row. 3+4+(4x15) = 67 ... any thoughts on my proof? Of course though I presented the logical reasoning for it, I didn't actually construct a mathematical or logical proof as such.