{"text_format":"3","workbook":"xlsx","n_sheets":4,"sheets":["Invert","All Weekdays","All Hours","Parts 0 to 17"],"not_rendered":{"macros":1,"defined_names":4,"comments":3},"read":"whole","date_system":"1900"}

{"sheet":"Invert","index":0,"n_rows":29,"n_cols":5,"rows_kept":29,"merged":[[8,0,11,0],[21,0,24,0]]}
["Inverting the Traditional Hebrew Calendar Molad",{"$nulls":3},"Parts"]
["by Dr. Irv Bromberg, University of Toronto, Canada",null,null,"Day",25920]
["http://individual.utoronto.ca/kalendis/hebrew/molad.htm#invert",null,null,"Hour",1080]
["For details refer to the cell formulae and see the Visual Basic for Applications (VBA) program code herein.",null,null,"Minute",18]
[]
["Given Weekday (Yom Rishon=1 ... Shabbat=7): ",5,null,"epoch",{"$f":"PartsPerDay*(2-1)+PartsPerHour*5+204","v":31524}]
["Given Hours (0-23): ",10,"count hours from zero = mean sunset (24h cycle)"]
["Given Parts (0-1079): ",111]
["Inverted Lunation Number: ",{"$f":"InvertMolad(B6,B7,B8)","v":60819},"fastest \"Direct Expression\" VBA Method (using an arithmetic formula)"]
[null,{"$f":"MOD(74377*((B6-1)*PartsPerDay+B7*PartsPerHour+B8-epoch),181440)","v":60819},"fastest \"Direct Expression\" using worksheet cell functions formula"]
[null,{"$f":"JumpSearchMolad(B6, B7, B8)","v":60819},"slower \"Jump Weekday\" Method (check every same weekday molad until found)"]
[null,{"$f":"SearchMolad(B6, B7, B8)","v":60819},"slowest \"Brute Force\" Method (check every molad until found)"]
["Hebrew Month and Year: ",{"$f":"LunationToYearMonthStr(B12)","v":"Shevat 4918"},"calculated from the inverted lunation number"]
["Next Match: ",{"$f":"LunationToYearMonthStr(B12+181440)","v":"Elul 19587"},"moladot repeat every 7 x 24 x 1080 = 181440 months (almost 14670 years)"]
[]
["or, with Minutes separated…"]
[]
[{"$f":"A6","v":"Given Weekday (Yom Rishon=1 ... Shabbat=7): "},7]
["Given Hours (0-23): ",20,{"$f":"C7","v":"count hours from zero = mean sunset (24h cycle)"}]
["Given Minutes (0-59): ",10]
["Given Parts (0-17): ",0]
[{"$f":"A9","v":"Inverted Lunation Number: "},{"$f":"InvertMoladHMP(B18,B19,B20,B21)","v":71472},"fastest \"Direct Expression\" VBA Method (using an arithmetic formula)"]
[null,{"$f":"MOD(74377*((B18-1)*PartsPerDay+B19*PartsPerHour+B20*PartsPerMinute+B21-epoch),181440)","v":71472},"fastest \"Direct Expression\" using worksheet cell functions formula"]
[null,{"$f":"JumpSearchMoladHMP(B18, B19, B20,B21)","v":71472},"slower \"Jump Weekday\" Method (check every same weekday molad until found)"]
[null,{"$f":"SearchMoladHMP(B18, B19, B20,B21)","v":71472},"slowest \"Brute Force\" Method (check every molad until found)"]
[{"$f":"A13","v":"Hebrew Month and Year: "},{"$f":"LunationToYearMonthStr(B25)","v":"Iyar 5779"},"calculated from the inverted lunation number"]
[{"$f":"A14","v":"Next Match: "},{"$f":"LunationToYearMonthStr(B25+181440)","v":"Tevet 20449"},"moladot repeat every 7 x 24 x 1080 = 181440 months (almost 14670 years)"]
[]
["Only the \"Direct Expression\" VBA Method will be employed for the other worksheets in this workbook."]

{"sheet":"All Weekdays","index":1,"n_rows":19,"n_cols":10,"rows_kept":19}
["Inverting the Traditional Hebrew Calendar Molad -- Weekday (Yom) Unknown"]
["by Dr. Irv Bromberg, University of Toronto, Canada"]
["http://individual.utoronto.ca/kalendis/hebrew/molad.htm#invert"]
[{"$f":"Invert!A4","v":"For details refer to the cell formulae and see the Visual Basic for Applications (VBA) program code herein."}]
[]
[null,null,"Hebrew Weekday: ","Yom Rishon","Yom Sheini","Yom Shlishi","Yom Rivii","Yom Chamishi","Yom Shishi","Yom Shabbat"]
[null,null,"Hebrew Yom #: ",1,2,3,4,5,6,7]
["Given Hours (0-23): ",0]
["Given Parts (0-1079): ",0]
[null,null,"Inverted Lunation Number: ",{"$f":"InvertMolad(D7,$B8,$B9)","v":88572},140412,10812,62652,114492,166332,36732]
[null,null,"Hebrew Month and Year: ",{"$f":"LunationToYearMonthStr(D10)","v":"Kislev 7162"},{"$f":"LunationToYearMonthStr(E10)","v":"Nisan 11353"},"Kislev 875","Nisan 5066","Av 9257","Kislev 13449","Av 2970"]
[null,null,"Next Match: ",{"$f":"LunationToYearMonthStr(D10+181440)","v":"Tammuz 21831"},{"$f":"LunationToYearMonthStr(E10+181440)","v":"Cheshvan 26023"},"Av 15544","Kislev 19736","Adar Sheini 23927","Tammuz 28118","Adar Sheini 17640"]
["or, with Minutes separated…"]
["Given Hours (0-23): ",0]
["Given Minutes (0-59): ",0]
["Given Parts (0-17): ",0]
[null,null,"Inverted Lunation Number: ",{"$f":"InvertMoladHMP(D7,$B14,$B15,$B16)","v":88572},140412,10812,62652,114492,166332,36732]
[null,null,"Hebrew Month and Year: ",{"$f":"LunationToYearMonthStr(D17)","v":"Kislev 7162"},{"$f":"LunationToYearMonthStr(E17)","v":"Nisan 11353"},{"$f":"LunationToYearMonthStr(F17)","v":"Kislev 875"},{"$f":"LunationToYearMonthStr(G17)","v":"Nisan 5066"},{"$f":"LunationToYearMonthStr(H17)","v":"Av 9257"},{"$f":"LunationToYearMonthStr(I17)","v":"Kislev 13449"},{"$f":"LunationToYearMonthStr(J17)","v":"Av 2970"}]
[null,null,"Next Match: ",{"$f":"LunationToYearMonthStr(D17+181440)","v":"Tammuz 21831"},{"$f":"LunationToYearMonthStr(E17+181440)","v":"Cheshvan 26023"},"Av 15544","Kislev 19736","Adar Sheini 23927","Tammuz 28118","Adar Sheini 17640"]

{"sheet":"All Hours","index":2,"n_rows":34,"n_cols":9,"rows_kept":34}
["Inverting the Traditional Hebrew Calendar Molad -- Hours Unknown"]
["by Dr. Irv Bromberg, University of Toronto, Canada"]
["http://individual.utoronto.ca/kalendis/hebrew/molad.htm#invert"]
[{"$f":"Invert!A4","v":"For details refer to the cell formulae and see the Visual Basic for Applications (VBA) program code herein."}]
[]
[{"$nulls":7},"Given Weekday (1 to 7): ",6]
[null,null,"Given Weekday (1 to 7): ",6,{"$nulls":3},"Given Minutes (0-59): ",13]
[null,null,"Given Parts (0-1079): ",31,{"$nulls":3},"Given Parts (0-17): ",5]
[]
["Hour","Lunation","Hebrew Month and Year","Next Match",null,"Hour","Lunation","Hebrew Month and Year","Next Match"]
[0,{"$f":"InvertMolad(D$7,A11,D$8)","v":113299},{"$f":"LunationToYearMonthStr(B11)","v":"Adar Rishon 9161"},{"$f":"LunationToYearMonthStr(B11+181440)","v":"Tishrei 23831"},null,{"$f":"A11","v":0},{"$f":"InvertMoladHMP(I$6,F11,I$8,I$7)","v":25243},{"$f":"LunationToYearMonthStr(G11)","v":"Elul 2041"},{"$f":"LunationToYearMonthStr(G11+181440)","v":"Iyar 16711"}]
[1,62539,{"$f":"LunationToYearMonthStr(B12)","v":"Adar Rishon 5057"},{"$f":"LunationToYearMonthStr(B12+181440)","v":"Tishrei 19727"},null,{"$f":"A12","v":1},155923,{"$f":"LunationToYearMonthStr(G12)","v":"Iyar 12607"},{"$f":"LunationToYearMonthStr(G12+181440)","v":"Kislev 27277"}]
[2,11779,"Adar Rishon 953","Tishrei 15623",null,2,105163,"Iyar 8503","Kislev 23173"]
[3,142459,"Tishrei 11519","Iyar 26188",null,3,54403,"Iyar 4399","Kislev 19069"]
[4,91699,"Tishrei 7415","Iyar 22084",null,4,3643,"Iyar 295","Kislev 14965"]
[5,40939,"Tishrei 3311","Iyar 17980",null,5,134323,"Kislev 10861","Av 25530"]
[6,171619,"Iyar 13876","Tevet 28546",null,6,83563,"Kislev 6757","Av 21426"]
[7,120859,"Iyar 9772","Tevet 24442",null,7,32803,"Kislev 2653","Av 17322"]
[8,70099,"Iyar 5668","Tevet 20338",null,8,163483,"Av 13218","Adar 27888"]
[9,19339,"Iyar 1564","Tevet 16234",null,9,112723,"Av 9114","Adar 23784"]
[10,150019,"Tevet 12130","Av 26799",null,10,61963,"Av 5010","Adar 19680"]
[11,99259,"Tevet 8026","Av 22695",null,11,11203,"Av 906","Adar 15576"]
[12,48499,"Tevet 3922","Av 18591",null,12,141883,"Adar 11472","Cheshvan 26142"]
[13,179179,"Av 14487","Adar Sheini 29157",null,13,91123,"Adar 7368","Cheshvan 22038"]
[14,128419,"Av 10383","Adar Sheini 25053",null,14,40363,"Adar 3264","Cheshvan 17934"]
[15,77659,"Av 6279","Adar Sheini 20949",null,15,171043,"Cheshvan 13830","Sivan 28499"]
[16,26899,"Av 2175","Adar Sheini 16845",null,16,120283,"Cheshvan 9726","Sivan 24395"]
[17,157579,"Adar Sheini 12741","Cheshvan 27411",null,17,69523,"Cheshvan 5622","Sivan 20291"]
[18,106819,"Adar Sheini 8637","Cheshvan 23307",null,18,18763,"Cheshvan 1518","Sivan 16187"]
[19,56059,"Adar Sheini 4533","Cheshvan 19203",null,19,149443,"Sivan 12083","Tevet 26753"]
[20,5299,"Adar Sheini 429","Cheshvan 15099",null,20,98683,"Sivan 7979","Tevet 22649"]
[21,135979,"Cheshvan 10995","Sivan 25664",null,21,47923,"Sivan 3875","Tevet 18545"]
[22,85219,"Cheshvan 6891","Sivan 21560",null,22,178603,"Tevet 14441","Elul 29110"]
[23,34459,"Cheshvan 2787","Sivan 17456",null,23,127843,"Tevet 10337","Elul 25006"]

{"sheet":"Parts 0 to 17","index":3,"n_rows":31,"n_cols":4,"rows_kept":31}
["Inverting the Traditional Hebrew Calendar Molad"]
["Parts of Minute (Chalakim) Unknown"]
["by Dr. Irv Bromberg, University of Toronto, Canada"]
["http://individual.utoronto.ca/kalendis/hebrew/molad.htm"]
[{"$f":"Invert!A4","v":"For details refer to the cell formulae and see the Visual Basic for Applications (VBA) program code herein."}]
[]
[null,null,"Given Weekday (1 to 7): ",6]
[null,null,"Given Hours (0-23): ",23]
[null,null,"Given Minutes (0-59): ",10]
[]
["Parts","Lunation","Hebrew Month and Year","Next Match"]
[0,{"$f":"InvertMoladHMP(D$7,D$8,D$9,A12)","v":48792},{"$f":"LunationToYearMonthStr(B12)","v":"Elul 3945"},{"$f":"LunationToYearMonthStr(B12+181440)","v":"Nisan 18615"}]
[1,123169,{"$f":"LunationToYearMonthStr(B13)","v":"Adar Rishon 9959"},{"$f":"LunationToYearMonthStr(B13+181440)","v":"Tishrei 24629"}]
[2,16106,"Tevet 1303","Av 15972"]
[3,90483,"Sivan 7316","Shevat 21986"]
[4,164860,"Kislev 13330","Tammuz 27999"]
[5,57797,"Tishrei 4674","Iyar 19343"]
[6,132174,"Adar 10687","Cheshvan 25357"]
[7,25111,"Shevat 2031","Elul 16700"]
[8,99488,"Tammuz 8044","Shevat 22714"]
[9,173865,"Tevet 14058","Av 28727"]
[10,66802,"Cheshvan 5402","Sivan 20071"]
[11,141179,"Nisan 11415","Kislev 26085"]
[12,34116,"Shevat 2759","Tishrei 17429"]
[13,108493,"Av 8772","Adar 23442"]
[14,1430,"Sivan 116","Tevet 14786"]
[15,75807,"Cheshvan 6130","Tammuz 20799"]
[16,150184,"Iyar 12143","Kislev 26813"]
[17,43121,"Adar 3487","Tishrei 18157"]
[]
["Weekday and Hours with Parts unknown would require 1080 rows."]