my math teacher died in a early time, I quitScorpiour wrote:
Quiz #3
there are 9 positive numbers as a sequence with a formula of general term
post the 10th number ( you needn't to write out the formula )
one person one post, no edit allowed
320057779
45232
10004921
81263099
190134
319944613
55815655
326755503
56536998
..?
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123456788
owh.. yea.. atama ga itai... yo... i can die by facerollsChloe wrote:
my math teacher died in a early time, I quitScorpiour wrote:
Quiz #3
there are 9 positive numbers as a sequence with a formula of general term
post the 10th number ( you needn't to write out the formula )
one person one post, no edit allowed
320057779
45232
10004921
81263099
190134
319944613
55815655
326755503
56536998
..?
111111111！
151430771
15175731
The answer should be 123456788 and the reason is here.
SPOILER
Well they are all roots of this equation
x^10-1294070722 x^9+667395555810652935 x^8-175697917976151422544451332 x^7+25361037237788364366816447004541667 x^6-2036252191926266620345699457610392414631090 x^5+87619632102485100661167183211502861408006268750065 x^4-1772117174931041816014099013237349419378055049276549654328 x^3+11011330627551295002347288664176730257951626517341003284662497572 x^2-2509547295261047511704607969010248172767105081297698303882340184749648 x+91147017802460151881398738157853197176173298245817673626627442414227280640=0
x^10-1294070722 x^9+667395555810652935 x^8-175697917976151422544451332 x^7+25361037237788364366816447004541667 x^6-2036252191926266620345699457610392414631090 x^5+87619632102485100661167183211502861408006268750065 x^4-1772117174931041816014099013237349419378055049276549654328 x^3+11011330627551295002347288664176730257951626517341003284662497572 x^2-2509547295261047511704607969010248172767105081297698303882340184749648 x+91147017802460151881398738157853197176173298245817673626627442414227280640=0
夢消失……Scorpiour wrote:
Quiz #3
there are 9 positive numbers as a sequence with a formula of general term
post the 10th number ( you needn't to write out the formula )
one person one post, no edit allowed
320057779
45232
10004921
81263099
190134
319944613
55815655
326755503
56536998
..?
随便猜一个好了
806628686
123456788
123456789
The nth term of the sequence is equal to b(n), where b(n) denotes a blahpy number. The 10th term of the sequence is 335833314.
The first few blahpy numbers are defined as:
b(1) = 320057779
b(2) = 45232
b(3) = 10004921
b(4) = 81263099
b(5) = 190134
b(6) = 319944613
b(7) = 55815655
b(8) = 326755503
b(9) = 56536998
b(10) = 335833314
The first few blahpy numbers are defined as:
b(1) = 320057779
b(2) = 45232
b(3) = 10004921
b(4) = 81263099
b(5) = 190134
b(6) = 319944613
b(7) = 55815655
b(8) = 326755503
b(9) = 56536998
b(10) = 335833314
123456788
123456788
123456788
简直为难人 我数学是体育老师教的你造么
简直为难人 我数学是体育老师教的你造么
19803508
I admit that's a good usage of your alias, whatever it actually means.blahpy wrote:
blahpy numbers
123456780
⑨
不算惹 太难，一张纸半管笔美丽
不算惹 太难，一张纸半管笔美丽
333566793
478294496
It doesn't mean anything lolnanda2009 wrote:
I admit that's a good usage of your alias, whatever it actually means.blahpy wrote:
blahpy numbers
I only just remembered this puzzle was here, looks like no-one found the actual solution yet though lol
333566793
~ 066606660 ~
*Fort runs
*Fort runs
Topic Starter
Quiz queue now:
First one is Mathematics:
The one who posts the correct answer first will earn a modding ticket from me
one person per post, no edit allowed!
First one is Mathematics:
The one who posts the correct answer first will earn a modding ticket from me
one person per post, no edit allowed!
k^3/8
Topic Starter
手误手误wmfchris wrote:
k^3/8
xyz = (k-x)(k-y)(k-z)
x = k-x
y = k-y
z = k-z
2x = k
2y = k
2z = k
x = k/2
y = k/2
z = k/2
xyz = (k^3)/8
i don't know about here but you want <= but = is part of <= i guess...
x = k-x
y = k-y
z = k-z
2x = k
2y = k
2z = k
x = k/2
y = k/2
z = k/2
xyz = (k^3)/8
i don't know about here but you want <= but = is part of <= i guess...
Topic Starter
if x=4, y=6 z=5 and k = 10, then?xxdeathx wrote:
xyz = (k-x)(k-y)(k-z)
x = k-x
y = k-y
z = k-z
2x = k
2y = k
2z = k
x = k/2
y = k/2
z = k/2
xyz = (k^3)/8
i don't know about here but you want <= but = is part of <= i guess...
x=kaa/(aa+bc)
y=kbb/(bb+ca)
z=kcc/(cc+ab)
然后我懒了
y=kbb/(bb+ca)
z=kcc/(cc+ab)
然后我懒了
It seems that when x=y=z=1/2k, it is the maximum of xyz, but I can't explain in detail to make a proof orz
设x+a=y+b=z+c=k，则xyz=abc
所以，根据均值定理，
k>=2*sqrt(xa)
k>=2*sqrt(yb)
k>=2*sqrt(zc)
所以k^3>=8*sqrt(xyzabc)
又xyz=abc
所以k^3>=8*(xyz)
所以xyz<=(k^3)/8
得证！
https://osu.ppy.sh/s/178495
所以，根据均值定理，
k>=2*sqrt(xa)
k>=2*sqrt(yb)
k>=2*sqrt(zc)
所以k^3>=8*sqrt(xyzabc)
又xyz=abc
所以k^3>=8*(xyz)
所以xyz<=(k^3)/8
得证！
https://osu.ppy.sh/s/178495
令Z≥X≥Y，所以XYZ的最大值为Z^3且等于(K-Z)的三次方
---> Z^3 = (K-Z)^3
---> Z=K-Z
---> Z=1/2K
所以Z^3=(1/2K)^3 , 这个是最大值
所以XYZ小于等于K^3/8
---> Z^3 = (K-Z)^3
---> Z=K-Z
---> Z=1/2K
所以Z^3=(1/2K)^3 , 这个是最大值
所以XYZ小于等于K^3/8
if x, y, z < k/2, substitute them into xyz to get xyz < k^3 / 8Scorpiour wrote:
if x=4, y=6 z=5 and k = 10, then?xxdeathx wrote:
xyz = (k-x)(k-y)(k-z)
x = k-x
y = k-y
z = k-z
2x = k
2y = k
2z = k
x = k/2
y = k/2
z = k/2
xyz = (k^3)/8
i don't know about here but you want <= but = is part of <= i guess...
if x, y, z > k/2, then k-x < k/2, k-y < k/2, k-z < k/2
then xyz = (k-x)(k-y)(k-z) < k^3 / 8
for effort...please?
As lgdry15 got the correct answer I will perform a standard trick towards the solution.
Let u = (k-x)/x, v = (k-y)/y, w = (k-z)/z (The case for x/y/z = 0 is obvious, so WLOG suppose they are positive.)
Then x = k/(u+1), y = k/(v+1), z = k/(w+1)
So that the equality becomes uvw = 1 and to show that (u+1)(v+1)(w+1) >= 8k^3.
Since u,v,w > 0, the result is obvious by AM-GM.
Let u = (k-x)/x, v = (k-y)/y, w = (k-z)/z (The case for x/y/z = 0 is obvious, so WLOG suppose they are positive.)
Then x = k/(u+1), y = k/(v+1), z = k/(w+1)
So that the equality becomes uvw = 1 and to show that (u+1)(v+1)(w+1) >= 8k^3.
Since u,v,w > 0, the result is obvious by AM-GM.
math is too hard =/
Topic Starter
lgdry15 got a modding ticket~~
and also thanks for other participants~
more quiz are coming
and also thanks for other participants~
more quiz are coming
Topic Starter
yeah i got this.. i didnt watch 2 months worth of anime for nothing..
wait jklols what is this ._.
wait jklols what is this ._.
OMG my mistake orz.
Name : Ore no imouto ga konna ni kawaii wake ga nai
Episode : 15
Season : 2010 / Season 4 ( autumn)
#1 Ore no Imouto ha Konna ni Kawaii Wake ga Nai episode 6 season 1
#2 Hyouka Episode 22 (I think there was only 1 season)
#3 Yosuga no Sora epsideo 9 (only 1 season)
#2 Hyouka Episode 22 (I think there was only 1 season)
#3 Yosuga no Sora epsideo 9 (only 1 season)
#1 俺の妹がんなに可愛 ep06
#2 Hyouka ep22
#3 Yosuga no Sora ep09
#2 Hyouka ep22
#3 Yosuga no Sora ep09
Topic Starter
correct~lightlance7 wrote:
#1 Ore no Imouto ha Konna ni Kawaii Wake ga Nai episode 6 season 1
#2 Hyouka Episode 22 (I think there was only 1 season)
#3 Yosuga no Sora epsideo 9 (only 1 season)
Nanako Kashii from toradora
mugi from k-on
Asuka from evangelion
mugi from k-on
Asuka from evangelion
Topic Starter
good~xxdeathx wrote:
Nanako Kashii from toradora
mugi from k-on
Asuka from evangelion
Prayer_old_1
im an overweight otaku living in basement watching anime 25 hours a day how do u expect me not to know any anime characterPrayer wrote:
omg how can these guys can know the answer. there's only stomach and breasts in the screenshots lol
jk i have my ways
:vxxdeathx wrote:
jk i have my ways
chokbar de bz
It's closed ye poofs
I laughed so hard XD well thanks for remindingPriti wrote:
It's closed ye poofs
Topic Starter
Switch to modding team queue now, check out the new modding rules please :>
wait so is it open?
my criteria:
- one post one map, no edit's allowed
- no other special rules, any style/artist/length/etc. of the song r fine to me.
- just one thing: my modding status might be various depend on the quality of your map check my mod to figure out how ur map's quality is
start NOW
5 slots open
5 slots open
http://osu.ppy.sh/s/180721 please owo~
closed
accpet:
smallbeans
Rtyzen
Kihhou
Aka
Gaia
thx guys, will mod them asap
accpet:
smallbeans
Rtyzen
Kihhou
Aka
Gaia
thx guys, will mod them asap
OPEN
5 slots
5 slots
https://osu.ppy.sh/s/194742
来个mod~~~~
来个mod~~~~
https://osu.ppy.sh/s/186450 NM please
Thanks
Thanks
CLOSED
accept:
Hinsvar
P o M u T a
kamisamaaa
Celizavia
ThEBonzi
accept:
Hinsvar
P o M u T a
kamisamaaa
Celizavia
ThEBonzi
o/, hope I can help you all
It's still CLOSE
my criteria:
- one post with one map, and don't edit.
- any maps is fine for me, but no horrible, I'm timid.
- sometimes, I'll make special rule (just for fun), please read my last post carefully.
- if you need mod in chinese, please tell me.
It's still CLOSE
OPEN
5 slots
5 slots