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!
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.
Cost: $232/cow
Total: $16704
total price = 16704
cow price = 232
$232/cow, for a total of $16,704
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?)
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!!!!!!
232 Cows $16704
$232 x 72 = $16704
ans is 16704 each cow price 232
Total $16704, per head price $232.
138431 was paid for each cow totaling 9967013
Make that $232/cow.
232* 72 = 16704
232 dollars for one,
1670 dollars in total.
*16704 for all
670 dollars for each and 48240 dollars altogether.
232 dollars per cow
total 16,704 dollars
$232 x 72 = $16,704
Answer is 16704
and each cow will cost 232
16704 is what I came up with –
232 for each cow, 16704 total?
$232 per cow for a total of $16704 paid for all 72.
@suineg, thanks, I have not been very active lately…the reason is that I have been stunned since Hex revealed the meaning of your name…:-)
Answer is 232 and 16704.
@dadeeo, your solution is amazing (138431 and 9967032), pretty good!!!
yes Bilbao, Hex blow away all the mystery surrounding my nickname
, but hey I explained why I put that nickname nothing to do with an over of 150 IQ like many of the usual visitors have, but cool man!!! Nice puzzle!!!
Thanks again for your submissions, Bilbao!
Hex reveals …
Hex blows away all the mystery surrounding…
Great newspaper headlines
Thanks to Bilbao for the challenging submissions.
Special thanks to RK (and ….olia) for this wonderful site and submissions.
Will anyone solve the mystery of “mashplum”?
each cow =$ 232
altogether = $16704
@Mashplum-enquiring minds want to know! Please tell!
@mashplum:
lums With Apples” baby food, perhaps?
Something to do with Gerber’s 2nd Foods “
@RK
Once again, I ask if there is a way for a user to turn off the “auto-smiley” feature when submitting comments.
Hey there Bobo, maybe I’ll just have the programmer disable the autosmiley feature, that’ll probably work best, thanks.
OK Bobo, autosmiley feature now disabled, thanks
Thanks, RK.
@mashplum, your name…anything to do with ‘World of Warcraft’?
hahaha…I am truly having fun giving a sense to your name…hahaha
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…..
@mashplum, and anything to do with P G Wodehouse’s nickname?…hahaha
Hi Chris Edwards, thank RK, our dungeon master.
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
@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!
@Chris Edwards, RK and his elves are responsible for the wonderful and challenging website.
We owe him a big thank you.
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 ; )
@RK, glad to be of help in your last point
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.
@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…
@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?
@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!!
@mashplum, looking forward to hearing from you…did I get any closer?
@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?
@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…
$16,704 total
$232 a piece
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.
So Mashplum is not selling an antique Gerber stock? >:>
RK, What happened to emoticons?
Not having the emoticons displayed could twist the tone of a statement from a simple joke to a flame.
It is a testament to the class of the posters on this site that nobody’s guesses involved testicular trauma. I thank you.
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.
I selected the >:> from the emoticons with the mouse, but I may have deleted some spaces??
test:
>:>
>:>
>:>
>:>
>:>
>:>
>:>
The red satan emoticon is out of order
testing
RK, are you trying to jinx me?
test:
>:>
test:
/>:>
/>>
testing
>:>
Each cow cost $232 72 each are 16704.
[...] The Unreadable Account [...]
232*72=16704