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# Mathematics Brain Teasers.

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On 10/8/2018 at 8:54 AM, danydandan said:

In a petri dish, there is a fungus. Every hour the fungus doubles in size. If it takes 48 hours for the fungus to cover the entire petri dish, how long would it take for the fungus to cover half of the petri dish?

The answer is: 47 hours. If it doubles in size every hour and fills the dish after 48 hours then one hour beforehand it was half the size and filled half the dish.

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2 minutes ago, Ozymandias said:

The answer is: 47 hours. If it doubles in size every hour and fills the dish after 48 hours then one hour beforehand it was half the size and filled half the dish.

Yeap.

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A baloon is inflated in such a way that its volume (V) is steadily increased 25% every second. Once full the process is precisely reversed and it is deflated. How long before it deflates to half its full volume?

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On 09/10/2018 at 3:31 PM, Ozymandias said:

A baloon is inflated in such a way that its volume (V) is steadily increased 25% every second. Once full the process is precisely reversed and it is deflated. How long before it deflates to half its full volume?

No takers? No interest?

Edited by Ozymandias
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7 minutes ago, Ozymandias said:

No takers? No interest?

7.

Probably not right, but was waiting to see if someone else wanted a go.

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3 minutes ago, danydandan said:

7.

Probably not right, but was waiting to see if someone else wanted a go.

No. Not 7. This teaser was harder than the previous ones and maybe there is no interest in the thread anyway.

Will wait till later before posting ghe solution.

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7 minutes ago, Ozymandias said:

No. Not 7. This teaser was harder than the previous ones and maybe there is no interest in the thread anyway.

Will wait till later before posting ghe solution.

The rate if change is 25% per minute.

So I was thinking.

0-0%

1-25%

2-50%

3-75%

4-100%

5-100%

6-75%

7-50%

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27 minutes ago, danydandan said:

The rate if change is 25% per minute.

So I was thinking.

0-0%

1-25%

2-50%

3-75%

4-100%

5-100%

6-75%

7-50%

You can't start from zero volume for two reasons. One, a deflated balloon has volume. Two, if it had not volume, increasing zero by 25% gives zero! In any case the question is really about the deflation process so you start from the fully inflated volume which you just call V. The exact reverse of increasing by 25% every second is to decrease by 20% every second. Therefore, starting with full inflation V at time zero, the volume after 1 second is 0.8V, and after the next second is 0.8[(0.8)V] = [(0.8)^2]V, then after the third second is [(0.8)^3]V, etc .....

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58 minutes ago, Ozymandias said:

You can't start from zero volume for two reasons. One, a deflated balloon has volume. Two, if it had not volume, increasing zero by 25% gives zero! In any case the question is really about the deflation process so you start from the fully inflated volume which you just call V. The exact reverse of increasing by 25% every second is to decrease by 20% every second. Therefore, starting with full inflation V at time zero, the volume after 1 second is 0.8V, and after the next second is 0.8[(0.8)V] = [(0.8)^2]V, then after the third second is [(0.8)^3]V, etc .....

Starting from full inflation volume (V) at time zero and a deflation rate of 20% we have:

V at t = 0

O.8V at t = 1

0.8(0.8V) = [(0.8)^2]V = 0.64V at t = 2

O.8(0.64)V = [(0.8)^3]V = 0.512 at t = 3

0.8(0.512)V = [(0.8)^4]V = 0.4096V at t = 4

The baloon's volume changes from 51.2% of fully inflated after 3 secs to 40.96% after 4 secs. So it reached 50% some time shortly after 3 seconds.

To determine the exact time we note that the deflation process is following an exponential decay with a rate of 0.8. This takes the form: v = V(0.8)^t where v is the volume at any time t and V is the starting volume.

At 50% full volume v = 0.5V so this equation becomes

0.5V = V(0.8)^t

0.5V/V = 0.8^t

0.5 = 0.8^t

log0.5 = t(log0.8)

t = (log0.5)/(log0.8)

t = (-3.0103)(-0.0969)

t = 3.1063 seconds to reach 50% of the fully inflated volume.

Edited by Ozymandias
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How can 10 plus the square root of 9 plus the square root of 4 equal 5?

10 + sqrt(9) + sqrt(4) = 5 ???

Edited by Ozymandias
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9 hours ago, Ozymandias said:

Starting from full inflation volume (V) at time zero and a deflation rate of 20% we have:

V at t = 0

O.8V at t = 1

0.8(0.8V) = [(0.8)^2]V = 0.64V at t = 2

O.8(0.64)V = [(0.8)^3]V = 0.512 at t = 3

0.8(0.512)V = [(0.8)^4]V = 0.4096V at t = 4

The baloon's volume changes from 51.2% of fully inflated after 3 secs to 40.96% after 4 secs. So it reached 50% some time shortly after 3 seconds.

To determine the exact time we note that the deflation process is following an exponential decay with a rate of 0.8. This takes the form: v = V(0.8)^t where v is the volume at any time t and V is the starting volume.

At 50% full volume v = 0.5V so this equation becomes

0.5V = V(0.8)^t

0.5V/V = 0.8^t

0.5 = 0.8^t

log0.5 = t(log0.8)

t = (log0.5)/(log0.8)

t = (-3.0103)(-0.0969)

t = 3.1063 seconds to reach 50% of the fully inflated volume.

Didn't even consider that solution. I'll stick my mathematics hat on from now on.

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8 hours ago, Ozymandias said:

How can 10 plus the square root of 9 plus the square root of 4 equal 5?

10 + sqrt(9) + sqrt(4) = 5 ???

10+(-3)+(-2)=5

Only way I can think. Can we substitute thhe sum?

Because conventionally square root means positive. So it's kinda unconventional.

Edited by danydandan
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Just now, danydandan said:

10+(-3)+(-2)=5

Only way I can think.

That's it! Most people only consider the positive square roots of numbers. Your turn to set a teaser.

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7 minutes ago, Ozymandias said:

That's it! Most people only consider the positive square roots of numbers. Your turn to set a teaser.

What's weird is, my initial thought was to do that. Then I thought thats too easy, I'll change to a different modulo, that was too annoying so I thought I'll convert to a different base, too much work. Then I thought maybe 10=1.0=0, thus the positive roots are good. But in the end you earlier said your questions aren't devious.

So negative square roots it is.

My teaser.

9 1 5

4 8 3

2 x 7

X=?

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4 hours ago, danydandan said:

My teaser.

9 1 5

4 8 3

2 x 7

X=?

These numbers are generated from the digits on a standard phone keypad. Each group of three numbers has been read diagonally from bottom right up to top left in the order 1st, 3rd, 2nd.

4     5     6     4     5     6     4     5         4     5     6

7    8     9     7     8     9     7     8     9         8     9

1     2     3     1     2     3         2     3     1     2     3

4     5     6     4     5     6     4     5     6     4     5     6

7     8     9     7     8     9     7     8     9     7     8     9

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17 minutes ago, Ozymandias said:

These numbers are generated from the digits on a standard phone keypad. Each group of three numbers has been read diagonally from bottom right up to top left in the order 1st, 3rd, 2nd.

4     5     6     4     5     6     4     5         4     5     6

7    8     9     7     8     9     7     8     9         8     9

1     2     3     1     2     3         2     3     1     2     3

4     5     6     4     5     6     4     5     6     4     5     6

7     8     9     7     8     9     7     8     9     7     8     9

Yeap 6 it is.

But I must say it's not for that above reason.

9+1+5=15

4+8+3=15

2+6+7=15

9+4+2=15

1+8+6=15

5+3+7=15

All diagonal and horizontal lines equal 15.

Edited by danydandan
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3 hours ago, danydandan said:

Yeap 6 it is.

But I must say it's not for that above reason.

9+1+5=15

4+8+3=15

2+6+7=15

9+4+2=15

1+8+6=15

5+3+7=15

All diagonal and horizontal lines equal 15.

Point taken.

My question:

This sequence of numbers is related to the alphabet : 4, 22, 9, 7, 2, 5, .....

What number comes next?

Edited by Ozymandias
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20 hours ago, Ozymandias said:

This sequence of numbers is related to the alphabet : 4, 22, 9, 7, 2, 5, .....

What number comes next?

Any takers? Will I give the answer?

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8 minutes ago, Ozymandias said:

Any takers? Will I give the answer?

Not yet!

Have not gotten a chance to work it out.

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3 minutes ago, danydandan said:

Not yet!

Have not gotten a chance to work it out.

OK!

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13 minutes ago, Ozymandias said:

OK!

Any hints? I'm thinking some sort of Affine cypher, but that is too much work if it isn't.

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Just now, danydandan said:

Any hints? I'm thinking some sort of Affine cypher, but that is too much work if it isn't.

Yes, a simple affline cypher leads to a string of letters that should be recognizable .... hence the solution.

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45 minutes ago, Ozymandias said:

Yes, a simple affline cypher leads to a string of letters that should be recognizable .... hence the solution.

I have used the decryption formula, where a is a co-prime number all the way up to 21 and where b is any number all the up to 15. I haven't gotten anywhere. That's using a=0, z=0, a=1 and z=1.

So I give up lol.

And I just wrote a brute force decryption code for Excel and I can't see anything either.?

Edited by danydandan
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A=1,B=0    DVIGBE
A=1,B=10    TLYWRU
A=1,B=11    SKXVQT
A=1,B=12    RJWUPS
A=1,B=13    QIVTOR
A=1,B=14    PHUSNQ
A=1,B=15    OGTRMP
A=1,B=16    NFSQLO
A=1,B=17    MERPKN
A=1,B=18    LDQOJM
A=1,B=19    KCPNIL
A=1,B=2    BTGEZC
A=1,B=20    JBOMHK
A=1,B=21    IANLGJ
A=1,B=22    HZMKFI
A=1,B=23    GYLJEH
A=1,B=24    FXKIDG
A=1,B=25    EWJHCF
A=1,B=3    ASFDYB
A=1,B=4    ZRECXA
A=1,B=5    YQDBWZ
A=1,B=6    XPCAVY
A=1,B=7    WOBZUX
A=1,B=8    VNAYTW
A=1,B=9    UMZXSV
A=11,B=0    FJWKTY
A=11,B=1    MQDRAF
A=11,B=10    XBOCLQ
A=11,B=11    EIVJSX
A=11,B=12    LPCQZE
A=11,B=13    SWJXGL
A=11,B=14    ZDQENS
A=11,B=15    GKXLUZ
A=11,B=16    NRESBG
A=11,B=17    UYLZIN
A=11,B=18    BFSGPU
A=11,B=19    IMZNWB
A=11,B=2    TXKYHM
A=11,B=20    PTGUDI
A=11,B=21    WANBKP
A=11,B=22    DHUIRW
A=11,B=23    KOBPYD
A=11,B=24    RVIWFK
A=11,B=25    YCPDMR
A=11,B=3    AERFOT
A=11,B=4    HLYMVA
A=11,B=5    OSFTCH
A=11,B=6    VZMAJO
A=11,B=7    CGTHQV
A=11,B=8    JNAOXC
A=11,B=9    QUHVEJ
A=15,B=0    VREQHC
A=15,B=1    OKXJAV
A=15,B=10    DZMYPK
A=15,B=11    WSFRID
A=15,B=12    PLYKBW
A=15,B=13    IERDUP
A=15,B=14    BXKWNI
A=15,B=15    UQDPGB
A=15,B=16    NJWIZU
A=15,B=17    GCPBSN
A=15,B=18    ZVIULG
A=15,B=19    SOBNEZ
A=15,B=2    HDQCTO
A=15,B=20    LHUGXS
A=15,B=21    EANZQL
A=15,B=22    XTGSJE
A=15,B=23    QMZLCX
A=15,B=24    JFSEVQ
A=15,B=25    CYLXOJ
A=15,B=3    AWJVMH
A=15,B=4    TPCOFA
A=15,B=5    MIVHYT
A=15,B=6    FBOARM
A=15,B=7    YUHTKF
A=15,B=8    RNAMDY
A=15,B=9    KGTFWR
A=17,B=0    RPCIXO
A=17,B=1    USFLAR
A=17,B=10    VTGMBS
A=17,B=11    YWJPEV
A=17,B=12    BZMSHY
A=17,B=13    ECPVKB
A=17,B=14    HFSYNE
A=17,B=15    KIVBQH
A=17,B=16    NLYETK
A=17,B=17    QOBHWN
A=17,B=18    TREKZQ
A=17,B=19    WUHNCT
A=17,B=2    XVIODU
A=17,B=20    ZXKQFW
A=17,B=21    CANTIZ
A=17,B=22    FDQWLC
A=17,B=23    IGTZOF
A=17,B=24    LJWCRI
A=17,B=25    OMZFUL
A=17,B=3    AYLRGX
A=17,B=4    DBOUJA
A=17,B=5    GERXMD
A=17,B=6    JHUAPG
A=17,B=7    MKXDSJ
A=17,B=8    PNAGVM
A=17,B=9    SQDJYP
A=19,B=0    HXKOLS
A=19,B=1    WMZDAH
A=19,B=10    BREIFM
A=19,B=11    QGTXUB
A=19,B=12    FVIMJQ
A=19,B=13    UKXBYF
A=19,B=14    JZMQNU
A=19,B=15    YOBFCJ
A=19,B=16    NDQURY
A=19,B=17    CSFJGN
A=19,B=18    RHUYVC
A=19,B=19    GWJNKR
A=19,B=2    LBOSPW
A=19,B=20    VLYCZG
A=19,B=21    KANROV
A=19,B=22    ZPCGDK
A=19,B=23    OERVSZ
A=19,B=24    DTGKHO
A=19,B=25    SIVZWD
A=19,B=3    AQDHEL
A=19,B=4    PFSWTA
A=19,B=5    EUHLIP
A=19,B=6    TJWAXE
A=19,B=7    IYLPMT
A=19,B=8    XNAEBI
A=19,B=9    MCPTQX
A=21,B=0    PBOEFU
A=21,B=1    KWJZAP
A=21,B=10    RDQGHW
A=21,B=11    MYLBCR
A=21,B=12    HTGWXM
A=21,B=13    COBRSH
A=21,B=14    XJWMNC
A=21,B=15    SERHIX
A=21,B=16    NZMCDS
A=21,B=17    IUHXYN
A=21,B=18    DPCSTI
A=21,B=19    YKXNOD
A=21,B=2    FREUVK
A=21,B=20    TFSIJY
A=21,B=21    OANDET
A=21,B=22    JVIYZO
A=21,B=23    EQDTUJ
A=21,B=24    ZLYOPE
A=21,B=25    UGTJKZ
A=21,B=3    AMZPQF
A=21,B=4    VHUKLA
A=21,B=5    QCPFGV
A=21,B=6    LXKABQ
A=21,B=7    GSFVWL
A=21,B=8    BNAQRG
A=21,B=9    WIVLMB
A=23,B=0    ZTGYRQ
A=23,B=1    ICPHAZ
A=23,B=10    LFSKDC
A=23,B=11    UOBTML
A=23,B=12    DXKCVU
A=23,B=13    MGTLED
A=23,B=14    VPCUNM
A=23,B=15    EYLDWV
A=23,B=16    NHUMFE
A=23,B=17    WQDVON
A=23,B=18    FZMEXW
A=23,B=19    OIVNGF
A=23,B=2    RLYQJI
A=23,B=20    XREWPO
A=23,B=21    GANFYX
A=23,B=22    PJWOHG
A=23,B=23    YSFXQP
A=23,B=24    HBOGZY
A=23,B=25    QKXPIH
A=23,B=3    AUHZSR
A=23,B=4    JDQIBA
A=23,B=5    SMZRKJ
A=23,B=6    BVIATS
A=23,B=7    KERJCB
A=23,B=8    TNASLK
A=23,B=9    CWJBUT
A=25,B=0    XFSUZW
A=25,B=1    YGTVAX
A=25,B=10    HPCEJG
A=25,B=11    IQDFKH
A=25,B=12    JREGLI
A=25,B=13    KSFHMJ
A=25,B=14    LTGINK
A=25,B=15    MUHJOL
A=25,B=16    NVIKPM
A=25,B=17    OWJLQN
A=25,B=18    PXKMRO
A=25,B=19    QYLNSP
A=25,B=2    ZHUWBY
A=25,B=20    RZMOTQ
A=25,B=21    SANPUR
A=25,B=22    TBOQVS
A=25,B=23    UCPRWT
A=25,B=24    VDQSXU
A=25,B=25    WERTYV
A=25,B=3    AIVXCZ
A=25,B=4    BJWYDA
A=25,B=5    CKXZEB
A=25,B=6    DLYAFC
A=25,B=7    EMZBGD
A=25,B=8    FNACHE
A=25,B=9    GOBDIF
A=3,B=0    BHUCJK
A=3,B=1    SYLTAB
A=3,B=10    PVIQXY
A=3,B=11    GMZHOP
A=3,B=12    XDQYFG
A=3,B=13    OUHPWX
A=3,B=14    FLYGNO
A=3,B=15    WCPXEF
A=3,B=16    NTGOVW
A=3,B=17    EKXFMN
A=3,B=18    VBOWDE
A=3,B=19    MSFNUV
A=3,B=2    JPCKRS
A=3,B=20    DJWELM
A=3,B=21    UANVCD
A=3,B=22    LREMTU
A=3,B=23    CIVDKL
A=3,B=24    TZMUBC
A=3,B=25    KQDLST
A=3,B=3    AGTBIJ
A=3,B=4    RXKSZA
A=3,B=5    IOBJQR
A=3,B=6    ZFSAHI
A=3,B=7    QWJRYZ
A=3,B=8    HNAIPQ
A=3,B=9    YERZGH
A=5,B=0    LZMWVG
A=5,B=1    QERBAL
A=5,B=10    JXKUTE
A=5,B=11    OCPZYJ
A=5,B=12    THUEDO
A=5,B=13    YMZJIT
A=5,B=14    DREONY
A=5,B=15    IWJTSD
A=5,B=16    NBOYXI
A=5,B=17    SGTDCN
A=5,B=18    XLYIHS
A=5,B=19    CQDNMX
A=5,B=2    VJWGFQ
A=5,B=20    HVISRC
A=5,B=21    MANXWH
A=5,B=22    RFSCBM
A=5,B=23    WKXHGR
A=5,B=24    BPCMLW
A=5,B=25    GUHRQB
A=5,B=3    AOBLKV
A=5,B=4    FTGQPA
A=5,B=5    KYLVUF
A=5,B=6    PDQAZK
A=5,B=7    UIVFEP
A=5,B=8    ZNAKJU
A=5,B=9    ESFPOZ
A=7,B=0    TDQMPI
A=7,B=1    EOBXAT
A=7,B=10    ZJWSVO
A=7,B=11    KUHDGZ
A=7,B=12    VFSORK
A=7,B=13    GQDZCV
A=7,B=14    RBOKNG
A=7,B=15    CMZVYR
A=7,B=16    NXKGJC
A=7,B=17    YIVRUN
A=7,B=18    JTGCFY
A=7,B=19    UERNQJ
A=7,B=2    PZMILE
A=7,B=20    FPCYBU
A=7,B=21    QANJMF
A=7,B=22    BLYUXQ
A=7,B=23    MWJFIB
A=7,B=24    XHUQTM
A=7,B=25    ISFBEX
A=7,B=3    AKXTWP
A=7,B=4    LVIEHA
A=7,B=5    WGTPSL
A=7,B=7    SCPLOH
A=7,B=8    DNAWZS
A=7,B=9    OYLHKD
A=9,B=0    JLYSDM
A=9,B=1    GIVPAJ
A=9,B=10    FHUOZI
A=9,B=11    CERLWF
A=9,B=12    ZBOITC
A=9,B=13    WYLFQZ
A=9,B=14    TVICNW
A=9,B=15    QSFZKT
A=9,B=16    NPCWHQ
A=9,B=17    KMZTEN
A=9,B=18    HJWQBK
A=9,B=19    EGTNYH
A=9,B=2    DFSMXG
A=9,B=20    BDQKVE
A=9,B=21    YANHSB
A=9,B=22    VXKEPY
A=9,B=23    SUHBMV
A=9,B=24    PREYJS
A=9,B=25    MOBVGP
A=9,B=3    ACPJUD
A=9,B=4    XZMGRA
A=9,B=5    UWJDOX
A=9,B=6    RTGALU
A=9,B=7    OQDXIR
A=9,B=8    LNAUFO
A=9,B=9    IKXRCL

Can't see anything that might suggest another letter to work backwards from. Sorry. Unless I'm making a big balls of it.