School-Safe Puzzle Games

The Unreadable Account

Much Thanks to Bilbao for submitting this!

Among certain accounts, partially blurred, the following can be read: ‘The amount paid for 72 cows was …670…dollars’. Two figures, the first and the last, are unreadable. It is known that every cow had the same price (no decimal places). How much was paid for each cow and altogether?

Answers to this challenge can be entered into the section below; submissions will automatically be revealed when time is up!

63 Comments to “The Unreadable Account”


  1. Jimmy Anders | PUZZLE MASTER | Profile

    If the sum is divisible by 72, then it is divisible by both 4 and 9. If a number is divisible by 4, then its last two digits must be divisible by 4, so the last digit is either 4 or 8. If a number is divisible by 9, then its digits must add to a multiple of 9. So if the last digit is 4 then the sum must be 16704 and if it’s 8, then the sum must be 66708.


    16704 / 72 = 232,
    66708 / 72 = 926.5.


    Since there was no decimal to the price of each cow, they each cost $232, adding up to $16704.


  2. Obsidian16 | Profile

    Cost: $232/cow
    Total: $16704


  3. Hex | PUZZLE MASTER | Profile

    total price = 16704
    cow price = 232


  4. Shawn | PUZZLE GRANDMASTER | Profile

    $232/cow, for a total of $16,704


  5. Bobo The Bear | PUZZLE MASTER | Profile

    Good puzzle!


    Two observations: The number ?670? must be even, limiting the possibilities for the last digit. Also, since 72 is a multiple of 9, ?670? must also be a multiple of 9, and its digits will add up to a multiple of 9. These observations reduce the options for ?670? to only 5 possibilities:


    56700
    36702
    16704
    86706
    66708


    Of these, only 16704 is a multiple of 72. And so:
    72 cows, at $232 each, cost $16704.


    (This assumes that the “$” symbol isn’t considered a figure, of course. There would be no solution for a four digit number 670?)


  6. suineg | PUZZLE MASTER | Profile

    Very nice puzzle Bilbao, starting to miss you man, but cool.


    Ok my solution to this puzzle is:
    Each cow cost 232 dollars so the cows altogether cost 16704 dollars.


    My way of solving it is not a neat path but I did not find any fancier way to solved it;


    ..DABC
    X..72
    .670.


    So you have this equations:


    1)7C + 2B + X = 0
    2)7B + 2A + Y = 7
    3)7A + 2D + Z = 6


    Then you have to try out values in equation number 1 that are consistents with equations 2 and 3.


    If C = 2 B = 3 and X = 0 you get that Y = 2 and A = 2
    and then you get that Z= 2 and D= 0


    Cool I know you guys will show me a neater way to do it but cool!!!!!!


  7. John Lewis Highsmith | Profile

    232 Cows $16704


  8. Adam | Profile

    $232 x 72 = $16704


  9. slimeball | Profile

    ans is 16704 each cow price 232


  10. cheddarmelt | Profile

    Total $16704, per head price $232.


  11. dadeeo | Profile

    138431 was paid for each cow totaling 9967013


  12. John Lewis Highsmith | Profile

    Make that $232/cow.


  13. Chris Edwards | Profile

    232* 72 = 16704


  14. Norway | Profile

    232 dollars for one,
    1670 dollars in total.


  15. Norway | Profile

    *16704 for all


  16. Fajri Umami | Profile

    670 dollars for each and 48240 dollars altogether.


  17. joe | Profile

    232 dollars per cow
    total 16,704 dollars


  18. Mashplum | PUZZLE MASTER | Profile

    $232 x 72 = $16,704


  19. kryz | Profile

    Answer is 16704
    and each cow will cost 232


  20. shaks | Profile

    16704 is what I came up with –


    232 for each cow, 16704 total?


  21. Kllr Wolf | Profile

    $232 per cow for a total of $16704 paid for all 72.


  22. bilbao | Profile

    @suineg, thanks, I have not been very active lately…the reason is that I have been stunned since Hex revealed the meaning of your name…:-)
    Answer is 232 and 16704.
    @dadeeo, your solution is amazing (138431 and 9967032), pretty good!!!


  23. suineg | PUZZLE MASTER | Profile

    yes Bilbao, Hex blow away all the mystery surrounding my nickname X| , but hey I explained why I put that nickname nothing to do with an over of 150 IQ like many of the usual visitors have, but cool man!!! Nice puzzle!!!


  24. RK | Founder | Profile

    Thanks again for your submissions, Bilbao!


  25. Hex | PUZZLE MASTER | Profile

    Hex reveals …
    Hex blows away all the mystery surrounding…


    Great newspaper headlines :D


    Thanks to Bilbao for the challenging submissions.


    Special thanks to RK (and ….olia) for this wonderful site and submissions.


  26. Mashplum | PUZZLE MASTER | Profile

    Will anyone solve the mystery of “mashplum”?


  27. condor2011 | Profile

    each cow =$ 232
    altogether = $16704


  28. RK | Founder | Profile

    @Mashplum-enquiring minds want to know! Please tell!


  29. Bobo The Bear | PUZZLE MASTER | Profile

    @mashplum:
    Something to do with Gerber’s 2nd Foods “;Plums With Apples” baby food, perhaps?


  30. Bobo The Bear | PUZZLE MASTER | Profile

    @RK
    Once again, I ask if there is a way for a user to turn off the “auto-smiley” feature when submitting comments.


  31. RK | Founder | Profile

    Hey there Bobo, maybe I’ll just have the programmer disable the autosmiley feature, that’ll probably work best, thanks.


  32. RK | Founder | Profile

    OK Bobo, autosmiley feature now disabled, thanks


  33. Bobo The Bear | PUZZLE MASTER | Profile

    Thanks, RK. :)


  34. bilbao | Profile

    @mashplum, your name…anything to do with ‘World of Warcraft’?
    hahaha…I am truly having fun giving a sense to your name…hahaha


  35. Chris Edwards | Profile

    thx 2 whomever is responsible for this site. I had an organ xplant a while back, and lost my marbles! This is a fun and not-too-stressful way to try to find my marbles again! so thx…..


  36. bilbao | Profile

    @mashplum, and anything to do with P G Wodehouse’s nickname?…hahaha


    Hi Chris Edwards, thank RK, our dungeon master.


  37. bilbao | Profile

    so my guess:
    world of warcraft master MAthias SHaw and p g wodehouse alias PLUM.
    I will let the others work out how I connected these to our mashplum


  38. Chris Edwards | Profile

    @Bilbao– thx for the response and the info. BTW, your ‘handle’ is almost the same as the name that I gave my very 1st car. My BFF’s car was named Frodo.


    Is RK responsible for the whole site? oh, yeah… just noticed the word “founder.” Ain’t I observant? Anyway, thanks RK et al!


  39. Hex | PUZZLE MASTER | Profile

    @Chris Edwards, RK and his elves are responsible for the wonderful and challenging website.


    We owe him a big thank you.


  40. RK | Founder | Profile

    The website wouldn’t be half as good if it weren’t for all the suggestions and puzzle submissions you guys provide!


    Plus, the quest for ever new and devious ways to torment you definitely keeps MY mind sharp ; )


  41. Hex | PUZZLE MASTER | Profile

    @RK, glad to be of help in your last point :D


  42. Mashplum | PUZZLE MASTER | Profile

    If I had known people would take this so seriously, I would have made it into its own puzzle!


    @Bobo, It’s nothing to do with baby food. I just needed an avatar.


    @bilbao Nothing to do with World of Warcraft. (I do play WoW, but I’ve never used mashplum as a character name. I’d be interested to know how you arrived at that guess.) The plum part has everything to do with P.G. Wodehouse’s nickname. But can anyone figure out why it’s mashplum? Hint: It’s kinda embarrassing.


  43. bilbao | Profile

    @Mashplum, I took this as a puzzle from the very beginning. I made a google search with ‘mashplum’ and tried to build up your alias from the two main issues among the results, which were WoW and PGWodehouse. I’m stuck right now, can’t find further explanations…


  44. Mashplum | PUZZLE MASTER | Profile

    @bilbao Ah-ha. I have used the name mashplum to post in Warcraft forums. That’s why it comes up in google. Did you investigate the Wodehouse links at all?


  45. bilbao | Profile

    @mashplum, I read a lot of things but not in depth. Anyway, I’ll make a last guess:
    from wiktionary, ‘mash (plural mashs)- (obsolete) the object of one’s affections’; is it that Wodehouse is your very favourite writer, up to the point that you write stories in Wodehouse style?. I’ll be offline till january. Happy Holidays!!


  46. bilbao | Profile

    @mashplum, looking forward to hearing from you…did I get any closer?


  47. Mashplum | PUZZLE MASTER | Profile

    @bilbao The “mash” comes from “mashup.” And yes, I did once write a story in the style of Wodehouse, which has a lot to do with it.


    btw, can I assume that your name comes from the city of Bilbao not a werid spelling of Bilbo Baggins?


  48. bilbao | Profile

    @mashplum, you are right. Nothing special about my name: it is the city where I live and it is also my last name (Txema Bilbao).I enjoyed very much the little investigation around your name…nice puzzle…


  49. Hendy | Profile

    $16,704 total
    $232 a piece


  50. Hendy | Profile

    It is very easy Mashplum clearly didn’t get enough of the Gerber product while learning to eat. Thus the name and the pic. Mystery solved. I’m partial to apricot, though.


  51. Hex | PUZZLE MASTER | Profile

    So Mashplum is not selling an antique Gerber stock? >:>


  52. Hex | PUZZLE MASTER | Profile

    RK, What happened to emoticons?


    Not having the emoticons displayed could twist the tone of a statement from a simple joke to a flame.


  53. Mashplum | PUZZLE MASTER | Profile

    It is a testament to the class of the posters on this site that nobody’s guesses involved testicular trauma. I thank you. ;)


  54. RK | Founder | Profile

    Hi there Hex, the emoticons are still available, but you have to hand select them with mouse from the ‘add emoticons’. Someone said the typed versions were causing problems, so just had the programmer remove.


  55. Hex | PUZZLE MASTER | Profile

    I selected the >:> from the emoticons with the mouse, but I may have deleted some spaces??


    test:
    >:>
    >:>
    >:>
    >:>
    >:>
    >:>
    >:>


  56. Hex | PUZZLE MASTER | Profile

    :D
    The red satan emoticon is out of order


  57. RK | Founder | Profile

    testing
    />:>
    />>)
    :sick


  58. Hex | PUZZLE MASTER | Profile

    RK, are you trying to jinx me? :D



    test:
    >:>


  59. Hex | PUZZLE MASTER | Profile

    test:
    />:>
    />>;)
    :sick


  60. Hex | PUZZLE MASTER | Profile

    testing
    >:>


  61. SubVet571 | Profile

    Each cow cost $232 72 each are 16704.


  62. bluekeremlin | Profile

    232*72=16704


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