function IsWhite(const balls, white: string; var calls: integer): boolean;
var
  i: integer;
begin;
  inc(calls);
  Result:=false;
  for i:=1 to Length(balls) do Result:=Result or (balls[i]=white[1]) or (balls[i]=white[2]);
  end;

function Find1(const balls, white: string; var calls: integer): char;
var
  half, count: integer;
begin;
  count:=Length(balls);
  half:=(count+1) shr 1;
  if count<=1
  then Result:=balls[1]
  else if IsWhite(copy(balls,1,half), white, calls)
       then Result:=Find1(copy(balls,1,half), white, calls)
       else Result:=Find1(copy(balls,1+half,count-half), white, calls);
  end;

function Find2(const balls, white: string; var calls: integer): string;
var
  i: integer;
begin;
  Result:='';
  for i:=1 to Length(balls)-1 do if IsWhite(balls[i], white, calls) then begin;
    Result:=Result+balls[i];
    if Length(Result)=2 then exit;
    end;
  Result:=Result+balls[Length(balls)];
  end;

function Find2From15(const balls, white: string; var calls: integer): string;
begin;
  if IsWhite('12345',white,calls)
  then if IsWhite('12f',white,calls)
       then if IsWhite('16',white,calls)
            then if IsWhite('89abcdef',white,calls)
                 then Result:='1'+Find1('89abcdef',white,calls)
                 else if IsWhite('3457',white,calls)
                      then Result:='1'+Find1('3457',white,calls)
                      else Result:=Find2('126',white,calls)
            else if IsWhite('cdef',white,calls)
                 then if IsWhite('f',white,calls)
                      then Result:=Find1('2345',white,calls)+'f'
                      else Result:='2'+Find1('cde',white,calls)
                 else Result:='2'+Find1('345789ab',white,calls)
       else if IsWhite('367',white,calls)
            then if IsWhite('4567',white,calls)
                 then if IsWhite('3',white,calls)
                      then Result:='3'+Find1('4567',white,calls)
                      else Result:=Find1('45',white,calls)+Find1('67',white,calls)
                 else Result:='3'+Find1('89abcde',white,calls)
            else if IsWhite('4',white,calls)
                 then Result:='4'+Find1('589abcde',white,calls)
                 else Result:='5'+Find1('89abcde',white,calls)
  else if IsWhite('6789',white,calls)
       then if IsWhite('abcd',white,calls)
            then Result:=Find1('6789',white,calls)+Find1('abcd',white,calls)
            else if IsWhite('ef',white,calls)
                 then Result:=Find1('6789',white,calls)+Find1('ef',white,calls)
                 else Result:=Find2('6789',white,calls)
       else if IsWhite('abcd',white,calls)
            then if IsWhite('ef',white,calls)
                 then Result:=Find1('abcd',white,calls)+Find1('ef',white,calls)
                 else Result:=Find2('abcd',white,calls)
            else Result:='ef';
  end;

function Validate: string;
const
  hex: array[0..15] of char= '0123456789abcdef';
var
  white, sol, maxsol: string;
  ch1, ch2: char;
  i, j, i1, i2, calls, maxcalls: integer;
begin;
  maxcalls:=0;
  for i2:=2 to 15 do begin;
    for i1:=1 to i2-1 do begin;
      white:=hex[i1]+hex[i2];
      calls:=0;
      sol:=Find2From15('abcd',white,calls);
      if maxcalls<calls then begin;
        maxcalls:=calls; maxsol:=sol;
        end;
      if white<>sol then begin;
        Result:=Format('Тест завален, неверное определение %s<>%s', [sol, white]);
        exit;
        end;
      end;
    end;
  Result:=Format('Тест пройден, максимум проверок %d для шаров %s', [maxcalls, maxsol]);
  end;