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[math puzzle] num 16

Blogs > evanthebouncy!
Post a Reply
evanthebouncy!
Profile Blog Joined June 2006
United States12796 Posts
Last Edited: 2009-11-29 20:51:05
November 29 2009 10:15 GMT
#1
I got this from a friend, it's pretty classic according to him
alpha and zetta had a flock of N sheeps
they sold them at N dollar each, for a total of N^2 dollars.
they put the dollars in a case.

alpha go to the case, and he took 10 dollars
zetta go to the case, and he took 10 dollars
...
... they alternate in taking moneys for awhile...
...
alpha go to the case, and he took 10 dollars
(a)zetta go to the case, and there is less than 10 dollars remaining, so he took the rest.
alpha made even with zetta by giving zetta some money

How much did zetta took from the case in step (a) ?

+ Show Spoiler [answer] +

I think the answer is 6, I'll be sure if someone come up with 6 as well. Here's justification:
Total number when modded by 20 has to be >10 since alpha took 10 then zetta has <10, which adds up to be >10.
Last trip zetta took less than 10 dollars
Total amount has to be even since alpha can make even
so the last bit of money has to be 2,4,6,8
no square number can end with 2 or 8, so it is either 4 or 6.
for a number to end in 4, and a square, we have N^2 = something4, then N has to end with 2.
N = (10n + 2)
N^2 = 100n^2 + 40n + 4, which, if modded by 20 has remainder of 4, which is not greater than 10.
Thus zetta took a final of 6 dollars.

edit:
I missed a case but the end solution does not change, thanks asharai!!

Hello,

For your math puzzle #16. There is something missing in the solution. A Square number N^2 ending by 4 means that either N ends by 2 or N ends by 8.

You missed the 8 case, although it can be removed with same reasons as for the 2 case.

Asharai


So I'll just put it in here, if it ends with 8, then
(10n+8)^2 = 100n^2 + 160n + 60 + 4
which also divides to less than 10 by 20.



I'll try to get people to rate my math blogs in terms of easiness
Please rate this blog 1 if you find it super hard, and rate it 5 if you find it super easy, or somewhere in between if it's not too hard or bad

GL HF! spoiler ur answer please! :D

***
Life is run, it is dance, it is fast, passionate and BAM!, you dance and sing and booze while you can for now is the time and time is mine. Smile and laugh when still can for now is the time and soon you die!
writer22816
Profile Blog Joined September 2008
United States5775 Posts
November 29 2009 10:30 GMT
#2
I smell a conspiracy to get higher rated blogs
8/4/12 never forget, never forgive.
TonyL2
Profile Blog Joined August 2007
England1953 Posts
November 29 2009 10:30 GMT
#3
I got the answer but differently :S

+ Show Spoiler +
30 dollars were taken. Zetta takes the remainder of less than 10. So a square number has to be between 30-40, which is 6
evanthebouncy!
Profile Blog Joined June 2006
United States12796 Posts
November 29 2009 10:35 GMT
#4
On November 29 2009 19:30 writer22816 wrote:
I smell a conspiracy to get higher rated blogs


but you see either way isn't it? Either the TL people think "Oh this is a shit blog rate it 1" or they think "LOL i'm so Smaaarrt~~"

by giving rating system this way they fuck themselves up either way.

In any regard i saw 2 votes for 5 which means this should be easy yet I only see 1 reply with real answer
Life is run, it is dance, it is fast, passionate and BAM!, you dance and sing and booze while you can for now is the time and time is mine. Smile and laugh when still can for now is the time and soon you die!
Yizuo
Profile Joined December 2004
Germany1537 Posts
November 29 2009 10:37 GMT
#5
Got the same solution with the same thinking .
I guess we're right!
evanthebouncy!
Profile Blog Joined June 2006
United States12796 Posts
November 29 2009 10:37 GMT
#6
On November 29 2009 19:30 TonyL2 wrote:
I got the answer but differently :S

+ Show Spoiler +
30 dollars were taken. Zetta takes the remainder of less than 10. So a square number has to be between 30-40, which is 6


oh by the "..." i meant they alternate taking money for potentially many many times, so the total dollar can be larger than 30.
i cleared it up now
Life is run, it is dance, it is fast, passionate and BAM!, you dance and sing and booze while you can for now is the time and time is mine. Smile and laugh when still can for now is the time and soon you die!
538
Profile Blog Joined November 2008
Hungary3932 Posts
Last Edited: 2009-11-29 10:42:18
November 29 2009 10:40 GMT
#7
On November 29 2009 19:30 writer22816 wrote:
I smell a conspiracy to get higher rated blogs

I felt some strange force compelling me to find this puzzle quite surprisingly hard.
BW fighting!
3clipse
Profile Blog Joined September 2008
Canada2555 Posts
November 29 2009 10:42 GMT
#8
On November 29 2009 19:40 538 wrote:
Show nested quote +
On November 29 2009 19:30 writer22816 wrote:
I smell a conspiracy to get higher rated blogs

I felt some strange force compeling me to find this puzzle quite surprisingly hard.

It's just awkwardly phrased. Once you realize what it's actually asking it's very basic math.
[ZiNC]Ling
Profile Blog Joined April 2009
United States69 Posts
November 29 2009 10:44 GMT
#9
Hmm, I like this problem but I was confused by
+ Show Spoiler +
the "must be even" conclusion, can't you split up an odd number of dollars evenly using cents??

After thinking about it though, there wouldn't be a single answer if you did that
evanthebouncy!
Profile Blog Joined June 2006
United States12796 Posts
November 29 2009 11:19 GMT
#10
On November 29 2009 19:44 [ZiNC]Ling wrote:
Hmm, I like this problem but I was confused by
+ Show Spoiler +
the "must be even" conclusion, can't you split up an odd number of dollars evenly using cents??

After thinking about it though, there wouldn't be a single answer if you did that


ah yeah dollars are unbreakable, didn't thhink people woiuld try to break dollars haha,
Life is run, it is dance, it is fast, passionate and BAM!, you dance and sing and booze while you can for now is the time and time is mine. Smile and laugh when still can for now is the time and soon you die!
freelander
Profile Blog Joined December 2004
Hungary4707 Posts
November 29 2009 11:32 GMT
#11
you confused me with the
"...
... they alternate in taking moneys for awhile...
..."

in your solution, you say they took 20xn dollar in this process but the text could say 10xn, cause it's not sure if the alternating happened even times

And all is illuminated.
Severedevil
Profile Blog Joined April 2009
United States4838 Posts
Last Edited: 2009-11-29 11:51:37
November 29 2009 11:50 GMT
#12
On November 29 2009 20:32 freelander wrote:
you confused me with the
"...
... they alternate in taking moneys for awhile...
..."

in your solution, you say they took 20xn dollar in this process but the text could say 10xn, cause it's not sure if the alternating happened even times


The relevant detail is that alpha was the first person to take $10 AND the last person to take $10, so there were $10 * odd# dollars initially. (Plus the less-than-$10 leftover that zetta took.)
My strategy is to fork people.
Essence
Profile Joined October 2005
165 Posts
November 29 2009 14:04 GMT
#13
6 it is for me as well
Cloud
Profile Blog Joined November 2004
Sexico5880 Posts
November 29 2009 15:06 GMT
#14
Oh that's cool, any perfect square of the form (10n + b) with n being odd and 0<b<10, needs b=6.
BlueLaguna on West, msg for game.
NarutO
Profile Blog Joined December 2006
Germany18839 Posts
November 29 2009 15:13 GMT
#15
Easy.. ^^
CommentatorPolt | MMA | Jjakji | BoxeR | NaDa | MVP | MKP ... truly inspiring.
evanthebouncy!
Profile Blog Joined June 2006
United States12796 Posts
November 30 2009 00:58 GMT
#16
last bump xD
Life is run, it is dance, it is fast, passionate and BAM!, you dance and sing and booze while you can for now is the time and time is mine. Smile and laugh when still can for now is the time and soon you die!
gyth
Profile Blog Joined September 2009
657 Posts
November 30 2009 16:02 GMT
#17
+ Show Spoiler +
To satisfy the conditions N^2 has to be odd in the tens place.
That only happens when N ends in a 4 or 6.
Both of which give an N^2 that ends in 6.
( 0 could give odd tens, but no remainder)

Is there always a solution if they were taking some amount other than 10?

I think the answer would be 1 if they took 8 at a time.
The plural of anecdote is not data.
Chronopolis
Profile Joined April 2009
Canada1484 Posts
February 06 2010 07:56 GMT
#18
Wow, I tried a good number of the puzzles and couldn't solve any X_X!! But it was fun mulling over the riddles. I was wondering why the puzzles suddenly end at this post. MOAR please!
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