more than one formula for 1) tables and 2) calculator shell
   

        # pretty print from autoindent and ased editor
        # Babylonian Brothers Inheritance Problems V2 Algorithm calculator
        # written on Windows XP on TCL
        # working under TCL version 8.6
        # gold on TCL Club, 25Nov2018
        package require Tk
        package require math::numtheory
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
        set tcl_precision 17
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} { initial and total estate (usually 60 shekels or 1 unit) :} }
        lappend names { number of brothers (b, usually 3-11) :}
        lappend names { next share fraction (usually 1-1/b, or else 1-1/c, or else 1+1/c)  : }
        lappend names { answers: elder brother : }
        lappend names { 2nd brother :}
        lappend names { 3ird brother : }
        lappend names { 4th brother : }
        lappend names { 5th brother   :}
        foreach i {1 2 3 4 5 6 7 8} {
            label .frame.label$i -text [lindex $names $i] -anchor e
            entry .frame.entry$i -width 35 -textvariable side$i
            grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 }
        proc about {} {
            set msg "Babylonian Brothers Inheritance Problems Algorithm V2
            from TCL
            # >>>>  Copyright Notice  <<<<<
            # This posting, screenshots, and TCL source code is
            # copyrighted under the TCL/TK 8.6 license terms.
            # Editorial rights retained under the TCL/TK license terms
            # and will be defended as necessary in court."
            tk_messageBox -title "About" -message $msg }
        proc self_help {} {
            set msg "Babylonian Brothers Inheritance Problems V2
            from TCL ,
            # self help listing
            # B. Inheritance  problem is using geometric progression
            # or possibly arithmetic/other progression
            # to calculate decreasing or increasing shares for
            # brothers, using Babylonian false position algorithm.
            # 3 givens follow.
            1) initial and total estate or principal, usually 60 silver pieces,
            1 unit, or field area.
            Usually field areas were <round numbers> in Babylonian units and usage.
            2) number of brothers or shares, b
            3) Entry N, usually for factor {1-1/brothers} for N brothers
            or else {1-1/constant} or else {1+1/constant} for alternate constant.
            Usually, Nth share is { elder brother share } * (1-1/b)**(N-1).
            # Some problems use alternate constant c rather than number of brothers.
            Most problems go down the staircase {1-1/b} from elder,
            but some problems go up the staircase using factor {1+1/b}
            or {1+1/c} starting with the youngest.
            # The Babylonians did not use modern algebraic notation,
            percent notation, modern units, or modern terminolgy.
            The interest solution from the clay tablets
            is a genuine antique method from 1600 BCE
            and different looking from modern math methods.
            The TCL solution is adapted from the
            clay tablets translated and explained by MCT,Friberg,Robson, etc.
            For the modern reader and comparisons with modern formulas,
            report may include percent notation, interest rate per annum,
            relative error in percent, meters, square meters, and other modern terms.
            The  TCL calculator solution is kept in { TCL precision 17 } to study
            the  Babylonian algorithms, not to imply accuracy beyond 3 decimal places
            or accuracy beyond the numbers on the clay tablets.
            Similarity to Babylonian interest rate formula,
            P&I =  expr (1+1/5.)**year
            # down the staircase
            first brother   X1
            second brother factor  (1-1/N),  (1-1/3), or  factor 0.666*X1.
            third brother  factor (1-1/N)*(1-1/N), (1-1/3)*(1-1/3) or factor 0.444*X1
            # up the staircase
            third brother X3
            second brother factor  (1+1/N),  (1+1/3) or  factor 1.333*X3.
            first brother  factor (1+1/N)*(1+1/N), (1+1/3)*(1+1/3) or factor 1.7777*X3
            # More than 5 brothers are overflow to the display slots
            # and shuffled to the report printout and list of brothers shares.
            # note: positive sign for (1+1/c) has to be switched or fudged in internal code.
            Answer check is sum of brother shares equals initial and total estate.
            The  TCL calculator solution is kept in { TCL precision 17 } to study
            the  Babylonian algorithms, not to imply accuracy beyond 3 decimal places
            or accuracy beyond the numbers on the clay tablets.
            Similarity to Babylonian interest rate formula,
            P&I =  expr (1+1/5.)**year
            However with base60 rounding and calculation slop,
            differences in results between the Babylonian year
            of 360 days and the modern year of 365 days are
            not usually discernable.
            # >>>>   Push Button Operation <<<<
            # Recommended procedure is push testcase and fill frame,
            # change first three entries etc, push solve,
            # and then push report. Report allows copy and paste
            # from console to conventional texteditor. For testcases,
            # the testcase number is internal to the calculator and
            # will not be printed until the report button is pushed
            # for the current result numbers.
            # Where the program defaults are recalled,
            # canvas colors/features/variables/globals/calculations/clear displays
            # are reset prior to calculation  ( in push button list) .
            # Buttons on the calculator are not limited to a single action procedure
            # or single shot. A button command may call multiple statements and procs,
            # effectively a separate program or subprogram installed as
            # a list of procedures in a button. Alternately, the list of procedures
            # need not be installed in a button, but in a separate procedure.
            Conventional text editor formulas or  grabbed from internet
            screens can be pasted into green console.
            Try copy and paste following into green screen console
            set answer [* 1. 2. 3. 4. 5. ] # answer returns 120
            set factor2 [ expr {(1-1./3)* (1-1./3)} ] # answer 0.4444
            set factor1 [ expr {(1+1./3)* (1+1./3)} ] # answer 1.7777
            set factor3 [ expr {(1-1./5)**5} ]  # answer 0.32768
            set factor4 [ expr {(1+1./5)**5} ]  # answer 4.21399
            # gold on  TCL Club, 25nov2018 "
            tk_messageBox -title "Self_Help" -message $msg }
        proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global testcase_number
            global real_scaled_results number_of_brothers check_if_constant_steps
            global average_all_brothers upper_bound lower_bound bound_constant_step
            global total_false_position scale_factor
            incr testcase_number
            set side1 [* $side1 1. ]
            set side2 [* $side2 1. ]
            set side3 [* $side3 1. ]
            set side4 [* $side4 1. ]
            set side5 [* $side5 1. ]
            set side6 [* $side6 1. ]
            set side7 [* $side7 1. ]
            set side8 [* $side8 1. ]
            set real_estate $side1
            set number_of_brothers $side2
            set integer_denominator2 $side3
            # initialize placeholder answer
            set result 1.
            set side4 0.
            set side5 0.
            set side6 0.
            set side7 0.
            set side8 0.
            #set brothers $number_of_brothers
            set decrement [/ 1. $integer_denominator2 ]
            set inheritance [** $number_of_brothers $number_of_brothers]
            set keeper [int [- $number_of_brothers 1] ]
            set keeperlist {}
            set i [int  $number_of_brothers ]
            set total_false_position 0.
            while {$i>0} {
                set inheritance [- $inheritance [* $inheritance $decrement]]
                if { $inheritance < 0 } { break }
                #set side$keeper $inheritance
                set keeperlist [ lappend keeperlist $inheritance ]
                set total_false_position [+ $total_false_position $inheritance  ]
                incr i -1
            }
            set scale_factor [/ $real_estate $total_false_position ]
            set counter 4
            set real_scaled_results {}
            foreach item $keeperlist {
                lappend real_scaled_results [* $item $scale_factor ]
                set side$counter [* $item $scale_factor ]
                incr counter
                if { [- $counter 4 ] > $number_of_brothers } {break}
            }
            # begin bounds and error checks
            set average_all_brothers [expr $real_estate/ $number_of_brothers  ]
            set upper_bound [+ $average_all_brothers [* 0.5 $average_all_brothers]]
            set lower_bound [- $average_all_brothers [* 0.5 $average_all_brothers]]
            set bound_constant_step [expr ($real_estate/ $number_of_brothers)/ ($number_of_brothers-1.) ]
            set check_if_constant_steps {}
            set counter5 0
            foreach item $keeperlist {lappend check_if_constant_steps [- $upper_bound [* $counter5 $bound_constant_step ]]
                incr counter5 }
        }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$aa"
            .frame.entry2 insert 0 "$bb"
            .frame.entry3 insert 0 "$cc"
            .frame.entry4 insert 0 "$dd"
            .frame.entry5 insert 0 "$ee"
            .frame.entry6 insert 0 "$ff"
            .frame.entry7 insert 0 "$gg"
            .frame.entry8 insert 0 "$hh"
        }
        proc clearx {} {
            foreach i {1 2 3 4 5 6 7 8 } {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global testcase_number
            global real_scaled_results number_of_brothers check_if_constant_steps
            global average_all_brothers upper_bound lower_bound bound_constant_step
            global total_false_position scale_factor
            console eval {.console config -bg palegreen}
            console eval {.console config -font {fixed 20 bold}}
            console eval {wm geometry . 40x20}
            console eval {wm title . " Babylonian Brothers Inheritance Report , screen grab and paste from console 2 to texteditor"}
            console eval {. configure -background orange -highlightcolor brown -relief raised -border 30}
            console show;
            puts "%|table $testcase_number|printed in| tcl format|% "
            puts "&| quantity| value| comment, if any|& "
            puts "&| $testcase_number:|testcase_number | |& "
            puts "&| $side1 :|initial and total estate (usually 60 shekels or 1 unit)   |   |&"
            puts "&| $side2 :|number of brothers | |& "
            puts "&| $side3 :|next share factor (usually 1-1/b, or else 1-1/c, or else 1+1/c) | |& "
            puts "&| $side4 :|answers: elder brother   | |&"
            puts "&| $side5 :|2nd brother | |&"
            puts "&| $side6 :|3ird brother |  |&"
            puts "&| $side7 :|4th brother  |  |&"
            puts "&| $side8 :|5th brother  |  |&"
            puts "&| $average_all_brothers :|for check, average_all_brothers |  |&"
            puts "&| $upper_bound  :|for check, upper_bound  |  |&"
            puts "&| $lower_bound :|for check, lower_bound  |  |&"
            puts "&| $bound_constant_step :|for check, bound_constant_step, if no 1/n less  |  |&"
            puts "&| $check_if_constant_steps :|for check, list bound_if_constant_steps, if no 1/n less  |  |&"
            puts "&| $total_false_position :|total false position |  |&"
            puts "&| [* $total_false_position $scale_factor]:|for check, total_false_position * sf =? initial real_estate | |&"
            puts "&| $real_scaled_results :|list of scaled brother shares  |  |&"
            # begin following for overflow brothers,  esp for brothers N > 5
            set counter 1
            if {$number_of_brothers > 5 } {puts "&| overflow table entries |overflow brothers, esp for N > 5  |  |&"}
            foreach item $real_scaled_results {
                if {$number_of_brothers < 6 } {break}
                puts "&| $item :|$counter nth brother  |  |&"
                incr counter 1
                if { $counter > $number_of_brothers } {break}}
            # end overflow section
        }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 60.   5.   5.0  17.  14.  11. 9. 7.0}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 120.  5.0  5.0  35.  28.  22. 18. 14.0 }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 3600. 5.0  5.0  1070. 856.  685. 548. 438.0 }
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command {about}
        ::ttk::button .self_help -text self_help -command {self_help}
        ::ttk::button .cons -text report -command { reportx }
        ::ttk::button .exit -text exit -command {exit}
        pack .calculator  -in .buttons -side top -padx 10 -pady 5
        pack  .clearallx .cons .self_help .about .exit .test4 .test3 .test2   -side bottom -in .buttons
        grid .frame .buttons -sticky ns -pady {0 10}
        . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
        wm title . "Babylonian Brothers Inheritance Problems Algorithm V2"