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Can You Solve This Math Riddle?

Can You Solve This Math Riddle?

A graphic shows a series of odd math equations and asks readers to fill in the final answer. How would you solve this equation and what answer do you think is best? Our readers have debated the problem for over 2 years.

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Math Riddle

First, let’s take a look at the riddle itself. The image below has circulated on social media for over two years. It contains the following math problem, often with a caption that reads:

We can’t figure this out… Can you? 92% of people fail it. Good luck!

1+5 = 12
2+10 = 24
3+15 = 36
5+25 = ?

After considerable debate here, we’ve come to the conclusion that there are four popular ways to solve this, resulting in two different answers.

Answer 1 – Pattern Theory

If we view the problem as a pattern, and not 4 separate math problems, then the answer to “5+25=” should be 60. If this is a pattern, then one row of the pattern was omitted. Consider looking at the problem this way:

1 5 12
2 10 24
3 15 36
4 20 48
5 25 60

If we view the equation in the manner above, then “4+20 = 48” was omitted from the original problem for reasons unknown. As you can see, however, the pattern theory holds that each column is its own pattern. The first column increases by 1, the second column increases by 5, and the third column increases by 12.

Answer 2 – Days and Weeks as Units

Math-ProblemAnother solution – which also yields an answer of 60  holds that the first two columns equal units of weeks and days respectively, and the third column represents days. Thus:

1 week + 5 days = 12 days
2 weeks + 10 days = 24 days
3 weeks + 15 days = 36 days
5 weeks + 25 days = 60 days

Answer 3 – Trick Question

If we look at the problem literally, then the answer to “5+25″should be 30. The logic here is that 3 incorrect answers in a row should not affect the answer to the problem posed to readers. Thus, 5+25 should be 30.

Answer 4 – Dr Dave’s Fibonacci series

As commenter DrDave points out below, this problem is a “Fibonacci series.” Even though he, too, comes up with 60 as an answer, his method is different than what we presented above. Although his explanation is in much more detail, perhaps the easiest way to look at it is to ignore the + and =, and just add the numbers in two columns to determine the next value. Thus:

1      5      12
+2   +10  +24
—————–
3      15    36

Then:

2      10     24
+3   +15  + 36
——————
5      25     60

Readers

The overwhelming opinion of commenters on our Facebook page is that the answer should be 60, although the ways of achieving answer this vary greatly.

Your Turn

What solution do you feel is the best to solve this problem? Do you have another theory that we didn’t pose here? Let us hear from you in the comments below.

Updated May 30, 2015
First published April 2013

  • Ryan

    1st numbers are all prime numbers hence no 4

  • mulla yasir ibrahim

    1+5=12 (1+5)2 =12
    2+10=24 (2+10)2 =24
    3+15=36 (3+15)2 =36
    4+20=48 (4+20)2 =48
    5+25=60 (5+25)2 =60

  • Goosie

    I’m in first grade and I an way smarter,
    1+5=12
    2+10=24
    3+15=36
    4+20=48
    5+25=60
    The first addend is by 1
    The second addend is by 5
    The answer is by 12

  • Eli Almoceda

    Let’s close this by saying 30 is most correct. Most people stick from simple to complex patterns and came out with something else. The question actually gave 3 wrong equations, forcing our minds to LOOK and IDENTIFY a pattern to make them RIGHT. Ask yourself this: Why is the supposed NEXT line “4+20=___” is MISSING? Are you sure that the pattern in mind is still valid even without this line? I guess not. Whatever pattern formed earlier simply disappeared. It’s like AB,BC,CD,E? where you insist “?” must be F saying that DE is implied, when the truth is, it’s NOT in the question.
    The fact remains that the pattern implied by the question was REMOVED at some point inside the question, leading us to 5+25 without any conditions to worry about.

  • Michael

    I received this as a post on FB, the solution I got was Longitude “60” Latitude “30” rounding the answer from the Baltic Sea to Russia. Due to current events (when I received the post), the Olympics were taking place. Then I Google Searched the image and found it was an old image that had nothing to do with current events. It looks like a think-inside-the-box solution.

  • Jordan

    From a teacher’s perspective, the answer is F:

    1+5=12 x (6)
    2+10=24 x (12)
    3+15=36 x (24)
    5+25= x (answer omitted)

    0 correct / 4 questions = F

  • Jordan

    I studied Pure Math in university. From a Purist’s perspective, here’s my answer:

    5+25=30

    You can all go back to sleep now…

  • kathleen

    From an artistic point of view 1 + 5 = 12 is blue, 2 + 10 = 24 is pink, 3 + 15 = 36 is yellow and 5 + 25 = ? is orange.

  • Claudiaa

    1 (2) + 5 (2)=12
    2 (10)+10 (2)=24
    3 (2)+15 (2)=36
    5 (2)+25 (2)=60

  • John Richards

    My answer is 96

    The numbers are multiples of 3. For example

    1 + 5 = 6 Take 12 and add them together you get 3.

    So the first line becomes:
    6 = 3

    The rest then works out as:

    12 = 6 (2+4)
    18 = 9 (3+6)
    24 = 12 (4 + 8)
    30 = 15 (9 + 6)

    hence my answer is 96

    Just adding to the debate!! 🙂

    • Jordan

      John: According to the pattern, the answer would be 69, not 96. In your first three examples, the lower number came first, but in the final example you flipped the order and put the big number first.

  • Sonja

    510, I think. See, its not even adding anything up, so much as looking at the number that comes out. If you’ll notice, the first digit is going by twos (2, 4, 6), while the second digit is going by ones (1, 2, 3). That is how you get 12, 24, and 36. Though it doesnt mattter as much, they are doing a similar thing with the addition part. The first number is counting by ones, and the second number is counting by fives. So the next equation after the last that they left out would be 4 + 20 = 48. But you don’t need to pay any attention to the addition part. It is only a distraction. All you need to do is (and this is starting from the point they left off, not what I added.) add 3+1=4+1=5 and 6+2=8+2=10, then combine the two numbers and you have 510. Now, one could also end up adding the 5 and 1 in 510, but I don’t think it sticks to the pattern, and so feel 510 is the best answer.

    1 | 5 | 1 \ 2
    2 | 10 | 2 \ 4
    3 | 15 | 3 \ 6
    (4 | 20 | 4 \ 8)
    5 | 25 | 5 \ 10

  • Felix

    So I’m a little late getting to this. I was actually looking for a different problem and came across this. The answer to the problem is subjective to the question itself. “We can’t figure this out… Can you?” is far too broad of a question. When given any question, however, you should never simply assume something. Since the question doesn’t specifically state “following the pattern, solve”, why would you? The value we are suppose to find is ?. And the equation is 5+25=?. Therefore, without assuming or doing anything more than what the question says, the answer would have to be 30.

  • MC

    My answer is 66 and it works

  • atousa

    Simpler form, add the 1 to the 5 gives you 6 multiply it by two you have 12, keep doing that you add both numbers then multiply by two

  • Henry Robinson

    It doesn’t ask for a pattern. It says, “Can you solve this riddle?” The answer is 30.

  • Henry Robinson

    Why is is NOT 60:

    1. Because 4 + 20 = 48 is not IN the problem. Therefore, it cannot be considered as part of it. In answer 1 you stated that it was omitted for reasons unknown. No, it was not omitted. It was never included and therefore cannot be used because then you would just be adding something into the problem to fit your theory. That would be the same as changing the wording of a test question so that it fits your answer. You can’t just add extra rows. With a math problem, you solve it based on what you are given, you can’t just add more things onto it, because then it isn’t even the same problem anymore.

    2. Because 5 + 25 doesn’t actually equal 60.

    3. Notice the word “then” is used. The word “if” was never used at the beginning.

    4. The word “Riddle” is used.

    Theories as to the answer: The answer can be one of 3 answers (depending if you’re going to decide whether or not to assume truths and throw things into it that were never part of the original problem)

    1. 30, because 5 + 25 = 30. Justification for this lies in the fact that it was never stated these equations are related, nor was the word “pattern” ever used in introducing this problem. The only word ever used for anyone to go on was “riddle.”

    2. 48, because the pattern is on the rightmost column and you’re supposed to ignore everything else. Look at it. 12, 24, 36, 48. If you’re looking for a pattern, there’s your pattern.

    3. There is no answer. This problem was designed in such a way that it cannot be solved because it is presented in a way that fails to provide you with any givens and/or truths to assume before beginning to attempt solving it.

  • JessieSun

    In base 4, numbers are going in this order: 1.number=1, 2.number=2, 3.number=3, 4.number=10, 5.number=11, 6.number=12, 7.number=13, 8.number=20, 9.number=21, 10.number=22, 11.number=23, 12.number=30, 13.number=31, 14.number=32, 15.number=33, 16.number=100, 17.number=101,… 25.number=121; so if 1+5=(1.number+5.number) in base 4=1+11=12 (in base10), 2+10=(2.number+10.number) in base 4=2+22=24 (in base10), 3+15=(3.number+15.number) in base 4=3+33=36 (in base10), then 5+25=(5.number+25.number) in base 4=11+121=132 (in base10) and answer is 132

  • steff

    1+5=12
    2+10=24
    3+15=36
    4+20=48
    5+25=60

    each of the answers are double what they should be
    1+5 should = 6
    2+10 should = 12
    3+15 should = 18
    4+20 should = 24
    5+25 should = 30

  • Coosh

    1+5= 12 is 2(1+5) = 12
    2+10=24 is 2(2+10) = 24
    3+15=36 is 2(3+15) = 36
    4+20=48 is 2(4+20) = 48
    5+25=60 is 2(5+25) = 60
    6+30=72 is 2(6+30) = 72
    7+35=84 is 2(7+35) = 84

  • Othmane

    Knowing the + is not the mathematical addition. Any theory that gets a credible result will be good.
    Here is mine :
    1+5=12
    2+10 = 24 (previous result + 2 + 10 = 12 + 2 + 10 = 24)
    3+15 = 36 (previous result + 3 + 15 = 24 + 3 + 15 = 36)
    4+20 = 60 (previous result + 4 + 20 = 36 + 4 + 20 = 60)
    5+25 = 90 (previous result + 5 + 25 = 60 + 5 + 25 = 90)

    Cheers.

    • DrDave

      @Othmane and @Paivi You’ve made the same mistake as several others by adding a 4 to the series in the left most column.

  • Päivi Viiri

    1+5=12 (1 and 2)
    2+10=24 (2 and 4)
    3+15=36 (3 and 6)
    4+20=48 (4 and 8)
    5+25=510 (5 and 10)

  • Bart

    (1) coupling = (2) individuals
    5c + 25c = 30c
    30 couplings = 60 individuals

  • David W

    Dr Dave – Its not even a “Fibonacci like series or sequence” Ha..

    Like I said before, “David W: All the additional perspectives and what people see, versus what is really there is a primary example why so many Crytos fail in deciphering codes and other secret information – they make it more complicated than it really is…”

    And that is why the obvious Fibonacci-like series is {NOT} the correct solution.

    • DrDave

      @David W: ‘Its not even a “Fibonacci like series or sequence” Ha..’ That is an interesting, but incorrect, observation you’ve made.

      A few of the values in the Fibonacci series

      0,1,1,2,3,5,8,13,21…
      Now let’s see, what are those values in the left column? Oh, of course
      1,2,3,5. Now where have I seen that series of values before?? OH-H-H-H-H…! Those are the 3rd through 6th values IN THE FIBONACCI SERIES!!! Hmmm, so I’m certain that the average person would agree that if there are 4 values in a list that are IDENTICAL to 4 values in the Fibonacci series that we can safely refer to the list as “Fibonacci-like”. And furthermore, when we see the method of obtaining the next value in the series is to add the previous two consecutive values, then ANY list that is formed in this manner, such as the middle column in the puzzle, can be referred to safely as “Fibonacci-like”.

      Perhaps you would be satisfied with “The solution of 60 can be derived by adding the previous two consecutive values in the list in the same manner that one produces the next value in the Fibonacci series, a portion of which is observed in the left column.”

  • David W

    DrDave – I took it upon myself to clear up and justify that in fact – This is NOT Fibonacci Series, Sequence or anything of the sort which you have fanatically suggested. As I stated the solution is 60 and only 60 and Pattern Theory. I contacted the Fibonacci Association and got an answer straight from the Horses mouth. Please read below and weep. And also as Karl noted, “arithmetic progressions” as I stated are “Pattern Theory” Below is Karl’s response..

    Hello David,

    Thank you for your interest in the Fibonacci Association.
    The “Math Teaser” file you attached is somewhat curious in that 1+5 is
    definitely not 12, so something must be missing. However, “arithmetic
    progressions” seem to be involved, so your solution of 60 is correct.
    However, I don’t see how the Fibonacci sequence could possibly entree.
    This sequence starts with 0 and 1, and every successive number in the
    sequence is the sum of the two previous numbers, giving 0, 1, 1, 2, 3, 5, 8, 13, 21, …

    A small note concerning terminology: The terms sequence and series are often used interchangeably, however “series” in mathematics means a sum that is either finite or (more often) infinite.

    I hope this reply helps.
    With best wishes,

    Karl Dilcher
    On-line Editor, The Fibonacci Quarterly

    • DrDave

      @David W: Perhaps you are “Fibonaccially challenged” LOL
      In any case, there is no need to even speak of the Fibonacci series to derive the answer of 60. I demonstrated that the next value in each column can be found be adding the two previous consecutive values. It just so happens that the left column is a PORTION of the Fibonacci series. I never said that the numbers AS PRESENTED were the Fibonacci series. Rather, that we can make some manipulations and SHOW the Fibonacci series can be produced in the left column.

      It is quite clear that neither you nor Karl Dilcher read my entire post. Look again. I said that using the GIVEN numbers in the puzzle, using the left column, work from the larger values to the smaller by SUBTRACTION of two consecutive values. This leads you BACKWARDS through the series to 0. Similarly, use ADDITION of two consecutive values to produce the next value, ad infinitum.

      5-3=2
      3-2=1
      2-1=1
      1-1=0

      So from the original
      1
      2
      3
      5
      We see that we can move backwards to
      0
      1
      1
      2
      3
      5
      It is OBVIOUS for those familiar with the Fibonacci series that we continue the series by adding the last two consecutive values. So the series continues as
      3+5=8
      5+8=13
      8+13=21
      13+21=34
      etc.
      Then, using this method of progression to the next value in the series by adding the previous two consecutive values, we move to the middle column and check to see if this method produces the results given in the original problem.

      middle column
      5
      10
      15
      25
      ==========
      5+10=15
      10+15=25. So indeed, this method does give the desired values. Therefore, we conclude this is the method of forming the next value in the sequence for each column. So applying this same method to the right column,
      which is given as

      right column
      12
      24
      36
      ?
      =====
      24+36=60. So 60 is the solution.

      Now that enables us to fill in values before and after those given in the problem to produce the following table
      ==============
      0 0 0
      1 5 12
      1 5 12
      2 10 24
      3 15 36
      5 25 60
      8 40 96
      13 65 156
      21 105 252
      34 170 408
      etc

      And CLEARLY, the left column is the Fibonacci series.

  • Emma

    This is impossible. Every answer falls down somewhere in the pattern. For example 60 doesn’t fit because the column that the 6 is in…the next number should be a 5 not a 6, but the answer 50 doesn’t work because 5+25 following the same pattern as the rest of the left side of the equation once multiplied by 2 is 60 and not 50. There are many possible answers…but none fit completely!!!

    • DrDave

      @Emma “There are many possible answers…but none fit completely!!!”

      Except the Fibonacci series solution.

  • Sid Hollander

    “And lo and behold, column 1 is our friendly Fibonacci series!”
    It would be more accurate to say that the given example contains 3 incomplete Fibonacci series (therefore not Fibonacci series) except that they do not show the initial terms of the series.

    The third column fails at the point “21+ 96= 250” Because the 250 should be 252 (96 + 156). The error is not corrected

    • DrDave

      @Sid,

      If you read all of the comments, you would have read that digits were transposed (56 instead of 65), so the middle column needs to be repaired from that point on. And now you have pointed out an arithmetic error in the right most column.

      However, these errors are inconsequential to the fact that the left column is a portion of the Fibonacci series, and, as I stated in the original post, the other two columns are formed “in the same manner”.

  • Stacey

    the pattern I see here is one of adding the current line with the one previous, so it would be:

    1 + 5 = 12
    + 2 + 10 = 24
    ———————–
    = 3 + 15 = 36

    therefore there would be not line with a four, it just carries on to be

    2 + 10 = 24
    + 3 + 15 = 36
    ———————–
    = 5 + 25 = 60

    • DrDave

      @Stacey
      Correct! Just as Fibonacci showed us to do.

  • David W

    DrDave,
    “And that is why the obvious Fibonacci-like series is the correct solution.”
    I beg to differ. Again, An equation is not needed when there is already a pattern. Nothing needed to be mathematically proved. It just is.. Because if “then” was not in the picture, your example would have not resulted in a correct answer.

  • MikeW

    OK, I got to the 510 that others got to, but did so slightly differently…

    Assume that the first number in the equation is the first digit/part of the answer. The second number in the equation is then divided by 2.5 to arrive at the second digit/part of the answer, as follows:
    1+5 : first digit = 1, second digit = 5 / 2.5 = 2, so the answer is 12
    2+10 : first digit = 2, second digit = 10 / 2.5 = 4, so the answer is 24
    3+15 : first digit = 3, second digit = 15 / 2.5 = 6, so the answer is 36
    5+25 : first digit = 5, second digit = 25 / 2.5 = 10, so the answer is 510

    • DrDave

      @Mike,
      Actually, your answer of 510 is not quite formulated correctly. Below is why it should be 60, not 510.

      25/2.5 =10. However, this cannot be use as a discrete value of “10”, but must be used as a right-most “0” with a “1” that is carried to the next left place. This results in the “first digit” as you called it being 6, because it is the PLUS the 1 that is carried over from the 10.

  • Thierry

    See the answers first:

    1+5 = 12
    2+10 = 24
    3+15 = 36
    5+25 = ?

    So,
    1+5 = 12 + 12
    2+10 = 24 + 12
    3+15 = 36 + 12
    5+25 = 48

    • DrDave

      @Thierry, your value of 48 would be for 4+20, not for 5+25. Then 5+25 =60. But as you see in the problem, the is no line of 4+20, so the progression by adding 12 is not correct. However, adding the previous two values to arrive at the next value does not have (and does not require) 4+20.

      See my explanation above on the Fibonacci series.

  • Esq

    5=11, so the answer is 66

  • Jeremy

    5 + 25 = 30 in every language
    Everything else is irrelevant ( wrong answers and plausable equations leading the question )

    • Jeremy

      I would also like to add in :

      92% of people get this wrong, from what Ive seen, most come up with 60
      Therefore the highest number of people all answering 60 dictates that 92% rule, therefore 60 is wrong.

  • David W

    Answer 1 – Pattern Theory is the only rational rule to derive the answer 60 UNLESS 5+25=? begins another pattern of criteria for rules not shown. However that is not the case, as “then” denotes a question to the observer If these rule = this, then what would 5+25=? The only tease is the missing 4th pattern level. Each number is separated by operand having clarified themselves as direct rule pattern. row 1 – 1, 2, 3, 4, 5 [increasing by 1] operand row 2- 5,10,15… [increasing by 5] operand row 3 – 12,24,36 [increasing by 12] The only way 5+25= would = something other than 60 is 1. – if the qualifier “then” was not part of the chart and 2.- If 5+25= started a new set of rule pattern clarification. And both 1 and 2 scenarios do not exist so the only answer is 60. It does not continue, there are no other solutions. All the additional perspectives and what people see, versus what is really there is a primary example why so many Crytos fail in deciphering codes and other secret information – they make it more complicated than it really is..

    • DrDave

      “Davd W: All the additional perspectives and what people see, versus what is really there is a primary example why so many Crytos fail in deciphering codes and other secret information – they make it more complicated than it really is…”

      And that is why the obvious Fibonacci-like series is the correct solution.

  • J

    I got 72 lol.

    12 + 12 = 24 + 12 = 36 + 24 + 12 = 72

    Adnittedly I ignored everything on the left as it looked like a deliberate attemt to confuse the viewer. And thought that was the trick part to the question lol.

  • Cassandra

    LI just want to say I WAS WAY OFF. I said 48. Only because the sums have a difference of 12.
    12+12=24
    12+24=36
    12+36=48.

    I didn’t do the double thing. Lol. Oops.

  • Steve

    I treat it as an algebra question. With the first equation as 1+5=12. Suppose “5” is not a number but a variable so it’s less confusing we will change that variable name to “x”. So 1+x=12. And 2+10=24 with “2” as the variable so y+10=24. Solving for x and y then x= 11 and y=14 so 5+25 becomes x+xy=? Or x+x*y=? Which solves to 11 + 11*14=? Which is 165. Nothing states that a variable has to be a letter or Greek symbol. This premise only works of course is you assume the other numbers are actually numbers (base 10) and not variables themselves.

  • Will

    I looked at the pattern of how the sums were wrong and saw the 1st off by 6, the 2nd by 12, etc. So the pattern would make 5+25=60. But the simple answer was 5+25=30.

  • Raff

    I also came up with 510 but for a slightly different reason.

    The first digit in each number always increases by one and the second digit (increasing to two digits as the sequence goes to 10)is achieved by each increase of 5 equalling 2 therefore 1+5(2)=12, 2+10(4)=24, 3+15(6)=36, 4+20(8)=48, 5+25(10)=510

  • Nadirs

    (1+5)x2=12
    (2+10)x2=24
    (3+15)x2=36
    (4+20)x2=48
    (5+25)x2=60

    Boo!

  • Will

    This is not an “if” included before the “then”, which excludes this for a “solve the pattern” math problem. It’s a psychological problem with three wrong mathematical answers preceding a problem to solve. “5 + 25 = ?” The answer is simply 30.

    • chris

      Yup. I agree. And that’s the reason why 97% of y’all are getting this wrong. You’re over-thinking it. 5+25 is 30 regardless of whether the previous incorrect answers had a pattern or not.

  • nikki

    Well, if the + operator for each marks the first number as the first number in the answer and the second number as 5*n being decreased by 3 *n….. n, (5*n – 3*n) or n, n (2)

    1 + 5 = 12
    2 + 10 = 24
    3 + 15 = 36
    4 + 20 = 48
    5 + 25 = 510, 612, 714, 816, 918, 1020……

    I was a math major and tend to overthink things…… and I never assume an operator is what it seems to be….without clarification. :^)

    • nikki

      Where n are the fibonacci numbers….

      • nikki

        Nope. I take it back. Not fibonacci for this solution… (sorry)

  • DrDave

    Start at the bottom row and subtract row above to give next higher row
    col 1 col 2 col3
    5-3=2 25-15=10 ?-36=24 –> ? is 60
    3-2=1 15-10=5 36-24=12

    No need to make an insertion of an artificial row of 4+20=24
    Now if we continued this upwards and downwards, the table expands to this:
    0+ 0= 0
    1+ 5= 12
    ———————————————–
    1+ 5= 12
    2+ 10= 24
    3+ 15= 36
    5+ 25= 60
    8+ 40= 96
    13+ 56= 156
    21+ 96= 250
    34+152= 406
    55+248= 656
    89+400=1062
    ad infinitum
    1718

    And lo and behold, column 1 is our friendly Fibonacci series!
    The other two columns then can be be seen as being formed in the same manner as the Fibonacci series but rather than the series beginning 0,1,1 the second column begins 0,5,5 and the third column begins 0,12,12.

    The “+” and “=” have no more meaning than a space; they are simply space fillers that contribute to confusing the viewer.

    And there, good citizens, lies the true solution to the puzzle.
    (There are some more patterns in the individual digits that I won’t describe: I think your minds were bent sufficiently today with this revelation.)

    • waffles

      Thanks DrDave. We have updated the article to include your method.

      • waffles

        Where do you get 40?

        • Roine Göthberg

          6th line in the series the second column should read 65 not 56 thus the rest of the numbers in the second column is also wrong. That is further down the line than the 5 + 25 = ? though.

      • DrDave

        “Nadirs:your entire equation past this point is invalid.”

        HA-ha Nadirs. Transposed numbers don’t invalidate the series, it just means there needs to be a correction to the arithmetic for that column. The answer of 60 to the puzzle is correct as originally stated.

  • Maria H

    I Also think the answer can be 510! But i’ve got an other solution.
    I see the pattern this way, the first number in every line is 1,2,3,(4),5
    In the second line from top to bottom is dubble the number before, 5,10,15,(20), 25
    Then in the third line you are back to 1,2,3(4), 5
    And in the last line you can se that the number is plussed by two every time, 2,4,6(8), 10
    This theory might not be wery mathematical correct But if you use it the answer is 510 and
    I think that couple be the right answer!

  • Jack D. Kammerer

    Another formation of it could create the answer 66, because using the word “then following” 3+15×2=36 THEN 5+25 could then create the answer to be 66…

  • Rebelwolf

    510.
    I interpreted the + as meaning ‘attach’, i.e. attach 1 to 2 and get 12. The pattern I saw was the 2nd number in each solution was the result of subtracting multiples of 3 from the 2nd number in each ‘sum’, i.e. 3 from the first (5-3=2), 6 from the second (10-6=4), 9 from the third (15-9=6).

    1+(5-3) = 12
    2+(10-6) = 24
    3+(15-9) = 36
    4+(20-12) = 48
    5+(25-15) = 510

    • jacob

      You could also use the first number as the 10’s and the second as the 1’s. Then you’d get 5*10+10*1 in the last one and also end up with 60 😉

  • Ady

    So on the basis that multiple patterns or formulas give multiple answers I would say its an impossible puzzle which was first published in 1969 so we could all be right or wrong as we don’t know the base against which the puzzle was established ?

    • waffles

      You may be onto something!

  • Patricia

    If the 3 equations are meant to be used, then it would be helpful to preface them with “if”, and so you would present an “if – then” problem. I think that would be helpful. Anyway, it was fun to do, and to see so many other responses from around the world. I don’t know what the percentage of correct answers is on Facebook, but it’s way more than 8%! P. S. According to your answer here, I did get the right answer (60), but kept wondering if there was another more complicated method to find the correct response… Thanks for posting!

    • Maths=no grey area

      But the correct answer is NOT 60 Patricia.

      The existence of 3 errors above the question in no way stops 5+25 equalling 30, any more than the existence of 3 purple elephants would. 5+25=30, and nothing else, (ever).

      On ‘IF’ statements
      There are no IF statements here, but even if there were, the answer could never be 60, at best it would still be 30, and it could possibly have no answer, since you never progress past the first IF statement (which is false, not true – as 1+5 does NOT equal 12), which means you never get as far as the word then, as doing so would require a true IF statement – though adding the word IF doesn’t even turn them into IF statements as they are all integers on both sides of the = without any variable).

      So, given that there are no IF statements the errors above the question should be ignored, for that is all they are – errors. They serve no purpose other than to fool people (and that is exactly why they are there). It seems to have worked 🙂

      In mathematics, all the answers in the universe are completely and utterly wrong, except for the one correct answer. 5+25=30 Every other answer in the universe is completely wrong. Love maths 🙂

      • Ken

        This is what I thought exactly. Math is infallible! It cannot be wrong and because there is no other information available to us, the answer is always 30. I try explaining this to my FB friends till I’m blue in the face but it’s like I’m talking to a wall!

  • Roine Göthberg

    Another way to look at it regarding patterns is that on the RHS the first digit increases by one and the second increases by two for every step. Thus the answer could also be 510. You could also reach this answer by looking at it in another way: first digit in answer equals first number in problem, second digit in answer equals second number in problem minus first number and divide it all by two. Works for every line.

    • nm

      1+5=12
      1+(5-(3*1))=12
      1+(5-3)=12
      2+(10-(3*2)) =24 2+(10-6)=24
      3+ (15-(3*3)) =36 3+(15-9)=36
      5+25=510
      5+(25-(3*5))=510 5+(25-15)=510
      So then the answer is 510
      😛

  • tim

    I saw this today and proposed a base 4 conversion solution

    1 + 5 (in base 10) = 6 (base 10) but is also 12 (in base 4)
    2 + 10 = 12 can be 24 (base 4) but technically should be 30
    3 + 15 = 18 and can be 36 (base 4) but should be 42
    5 + 25 = 30 can be 72 (base 4) technically 132

    • waffles

      We will defer to you on this one!

      • JusCravin

        Hello Waffle,
        The answer I came up with is 35 and the pattern was kept the same thank you.

    • Timothy Campbell

      Tim: I too tried various number bases, but I don’t understand your comments. You wrote, “2 + 10 = 12 can be 24 (base 4) but technically should be 30”

      I see what you did there. Let’s list the first bunch of digits in base 4 as a reference…

      0 1 2 3 10 11 12 13 20 21 22 23 30 31 32 33 100 101 102 103 110 …

      The clue says 2+10=24. So if we assume the 2+10 are in Base 10 we end up with 12 (also in base 10). If we then count off 12 positions on the Base-4 number line we arrive at “30” — just as you said.

      Now, somebody who doesn’t know how Base 4 works MIGHT say that the number after 23 is 24. But I don’t think it would be fair for a puzzle to propose a Base-4 number that can’t possibly exist.

      Your technique works perfectly for the first clue, but after that it doesn’t really seem to work. That’s why I gave up exploring a possible solution different bases and spotted the fact that it could all work out in Base 10 (see my first post).

      • waffles

        Ok Mr. Campbell, we’re going to seek your advice the next time we have a math problem 🙂

  • Timothy Campbell

    The following formula strikes me as the simplest solution…

    (First_Number + Second_Number) × 2 = Answer

    Thus:

    (1 + 5) × 2 = 12
    (2 + 10) × 2 = 24
    (3 + 15) × 2 = 36

    Therefore:

    (5 + 25) × 2 = 60

    • Carola

      That’s what I used, too.

    • ChrisB

      That is what I did also!

    • Nikhat

      1+5=12
      2+10=24
      3+15=36
      5+25=510
      FIRST digit. SAME RAHEGA JESE
      Sabse pehle 1-5=4, 4=2*2 =12
      2-10=8,8=4*2 =24
      3-15=12,12=6*2 =36
      5-25=20, 20=10*2 =510
      So right answer is 510/-

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