Ozymandias Posted October 9, 2018 #51 Share Posted October 9, 2018 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. Link to comment Share on other sites More sharing options...
danydandan Posted October 9, 2018 Author #52 Share Posted October 9, 2018 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. Link to comment Share on other sites More sharing options...
Ozymandias Posted October 9, 2018 #53 Share Posted October 9, 2018 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? Link to comment Share on other sites More sharing options...
Ozymandias Posted October 10, 2018 #54 Share Posted October 10, 2018 (edited) 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 October 10, 2018 by Ozymandias Link to comment Share on other sites More sharing options...
danydandan Posted October 10, 2018 Author #55 Share Posted October 10, 2018 7 minutes ago, Ozymandias said: No takers? No interest? 7. Probably not right, but was waiting to see if someone else wanted a go. Link to comment Share on other sites More sharing options...
Ozymandias Posted October 10, 2018 #56 Share Posted October 10, 2018 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. Link to comment Share on other sites More sharing options...
danydandan Posted October 10, 2018 Author #57 Share Posted October 10, 2018 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% Give me a radius lol. Link to comment Share on other sites More sharing options...
Ozymandias Posted October 10, 2018 #58 Share Posted October 10, 2018 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% Give me a radius lol. 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 ..... 1 Link to comment Share on other sites More sharing options...
Ozymandias Posted October 10, 2018 #59 Share Posted October 10, 2018 (edited) 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 October 10, 2018 by Ozymandias 1 Link to comment Share on other sites More sharing options...
Ozymandias Posted October 10, 2018 #60 Share Posted October 10, 2018 (edited) How can 10 plus the square root of 9 plus the square root of 4 equal 5? 10 + sqrt(9) + sqrt(4) = 5 ??? Edited October 10, 2018 by Ozymandias Link to comment Share on other sites More sharing options...
danydandan Posted October 11, 2018 Author #61 Share Posted October 11, 2018 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. Link to comment Share on other sites More sharing options...
danydandan Posted October 11, 2018 Author #62 Share Posted October 11, 2018 (edited) 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 October 11, 2018 by danydandan Link to comment Share on other sites More sharing options...
Ozymandias Posted October 11, 2018 #63 Share Posted October 11, 2018 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. Link to comment Share on other sites More sharing options...
danydandan Posted October 11, 2018 Author #64 Share Posted October 11, 2018 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. Link to comment Share on other sites More sharing options...
danydandan Posted October 11, 2018 Author #65 Share Posted October 11, 2018 My teaser. 9 1 5 4 8 3 2 x 7 X=? Link to comment Share on other sites More sharing options...
Ozymandias Posted October 11, 2018 #66 Share Posted October 11, 2018 4 hours ago, danydandan said: My teaser. 9 1 5 4 8 3 2 x 7 X=? The answer is 6. 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 6 4 5 6 7 8 9 7 8 9 7 8 9 7 8 9 1 2 3 1 2 3 1 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 1 Link to comment Share on other sites More sharing options...
danydandan Posted October 11, 2018 Author #67 Share Posted October 11, 2018 (edited) 17 minutes ago, Ozymandias said: The answer is 6. 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 6 4 5 6 7 8 9 7 8 9 7 8 9 7 8 9 1 2 3 1 2 3 1 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 October 11, 2018 by danydandan Link to comment Share on other sites More sharing options...
Ozymandias Posted October 11, 2018 #68 Share Posted October 11, 2018 (edited) 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 October 11, 2018 by Ozymandias Link to comment Share on other sites More sharing options...
Ozymandias Posted October 12, 2018 #69 Share Posted October 12, 2018 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? Link to comment Share on other sites More sharing options...
danydandan Posted October 12, 2018 Author #70 Share Posted October 12, 2018 8 minutes ago, Ozymandias said: Any takers? Will I give the answer? Not yet! Have not gotten a chance to work it out. Link to comment Share on other sites More sharing options...
Ozymandias Posted October 12, 2018 #71 Share Posted October 12, 2018 3 minutes ago, danydandan said: Not yet! Have not gotten a chance to work it out. OK! 1 Link to comment Share on other sites More sharing options...
danydandan Posted October 12, 2018 Author #72 Share Posted October 12, 2018 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. Link to comment Share on other sites More sharing options...
Ozymandias Posted October 12, 2018 #73 Share Posted October 12, 2018 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. Link to comment Share on other sites More sharing options...
danydandan Posted October 12, 2018 Author #74 Share Posted October 12, 2018 (edited) 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 October 12, 2018 by danydandan Link to comment Share on other sites More sharing options...
danydandan Posted October 12, 2018 Author #75 Share Posted October 12, 2018 A=1,B=0 DVIGBE A=1,B=1 CUHFAD 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=6 HREADW 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. Link to comment Share on other sites More sharing options...
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