Another Weird Test Question

I found this puzzle on Facebook:

Puzzle. Solve this:
1+4 = 5,
2+5 = 12,
3+6 = 21,
5+8 = ?
97% will fail this test.

Staring at this I decided on my answer. Then I looked at the comments: they were divided between 34 and 45 and didn’t contain the answer that initially came to my mind. The question to my readers is to explain the answers in the comments and suggest other ones. Can you guess what my answer was?

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25 Comments

  1. Martin Pedersen:

    32?

  2. Jo in OKC:

    If the pattern is that a+b = ab+a (or a(b+1) ) then 5+8 = 5*8+5 = 45.

    In base 5
    1+4 = 5
    2+5 = 12
    3+6 = 14
    So that works for the first 2 terms, but then fails for the 3rd.

  3. Oscar Cunningham:

    I was thinking 44. The first pair you multiply and add one, the second pair you multiply and add two, the third pair you multiply and add three, so in the fourth pair you multiply and add 4.

  4. calcdave:

    I saw the 45 first using a+b really meaning a*b+a which works for the other patterns.

  5. lvps1000vm:

    First line expresses the sum in base 6
    Second line expresses the sum in base 5
    Third line expresses the sum in base 4
    Therefore, fourth line expresses the sum in base 3, i.e. 111

    That’s my proposal.

  6. Joe:

    I can see the 45. For that answer, addition is the following operation: f(a,b) = a*(b+1).

  7. Jonathan Kariv:

    So like everyone else commenting I got 45 by a+b=a+a*b. Curious to know how people get to 34?

  8. Misha:

    object StrangeAddition extends App {
    implicit class StrangeInt(val a: Int) {
    def plus(b: Int): Int = a * (b + 1)
    }

    println(
    1 plus 4,
    2 plus 5,
    3 plus 6,
    5 plus 8,
    )
    }

  9. Gerhard:

    The first column lists the positive integers n=1,2,3,4,5,… (the line with n=4 has been skipped for some mysterious reason).
    The second column lists the values n+3.
    The third column lists the values (n+2)^2 – 4; it is all squares minus 4.

  10. Jesse O:

    I got 45 by the following reasoning: regard ‘+’ and ‘=’ as column separators. Then the pattern of the first column is to add 1, starting at 1. The pattern of the second column is to add 1, starting at 4. The pattern of the third column is to add successive odd numbers starting by adding 7 to 5. The fourth row is omitted from the puzzle.

  11. Geoff Dunstan:

    Clearly 45.

    1 + ! x $ = 5
    2 + 2 x 5 = 12
    3 + 3 x 6 = 21
    5 + 5 x 8 = 45

  12. Leif:

    You get to 34 by adding cumulatively:

    1 + 4 = 5
    (1 + 4) + 2 + 5 = 12
    (1 + 4 + 2 + 5) + 3 + 6 = 21
    (1 + 4 + 2 + 5 + 3 + 6) + 5 + 8 = 34

  13. Jonathan Kariv:

    @Leif Thanks

  14. CyberK:

    13? 😀

  15. Dave:

    37 also possible (as, really, is every number, if complicated functions are allowed). But this one is pretty simple:

    a+bN = answer for row N.

  16. RoyG:

    I got Dave’s answer. Intuitively the first solution I found. I guess our brains are wired differently.

  17. Dale:

    37

    It’s the simplest answer that works with the sequence.

    4×1
    5×2
    6×3
    7×4 +6 = 34

  18. Dale:

    LOL

    I even did the math wrong at the end, but the simplest answer still stands as 37.

  19. Jeroen:

    I can get to 44 (sum up all preceding numbers to the left):

    1 + 4 = 5
    + 2 + 5 = 12
    + 3 + 6 = 21
    + 5 + 8 = 44

    Though one could argue for 55 as well by adding the “missing” 4+7.

  20. Jeroen:

    Now if only I didn’t fail my basic math…

  21. Ted Ridgway:

    I think a proper solution should account for the missing “4+7” line. The first three lines establish the pattern. The reader has to extend it far enough to reach “5+8”. Fun fact – if you include +7, the two most popular algorithms both yield 45.
    More importantly, though – Tanya, what was your answer??

  22. tanyakh:

    My first thought was 111.

  23. Joseph:

    So the sums are 5 in base 6, 7 in base 5, 9 in base 4, and then 13 in base 3?

  24. Josué:

    En mi opinión, la aseveración de la sumas del puzzle tiene sentido cuando se multiplican los sumandos de la igualdad y después se suma el primer sumando a dicha multiplicación (en el orden en que están escritos en el rompecabezas). De esta forma.

    1 + 4 = 5 porque (1 • 4) + 1 = 5
    2 + 5 = 12 porque (2 • 5) + 2 = 12
    3 + 6 = 21 Porque (3 • 6) + 3 = 21
    5 + 8 = 45 Porque (5 • 8) + 5 = 45 Por tanto, 45 es mi respuesta.

    Disculpe el error de redacción de mi primer comentario.

  25. Ted Ridgway:

    I’ll stand by my idea that the “missing line” should be accounted for. So if we go for the representations in successively smaller bases …

    Given:
    1 + 4 = 5 (base 6)
    2 + 5 = 12 (base 5)
    3 + 6 = 21 (base 4)

    Then:
    4 + 7 = 102 (base 3)

    And the answer to question would be:
    5 + 8 = 1101 (base 2)

    Just my 10 cents.

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