Use the four digits 1, 9, 9, 7, in that order, with additions, subtractions, multiplication, division,...
arithmetic/digits/equations/1997 New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
Use the four digits 1, 9, 9, 7, in that order, with additions, subtractions, multiplication, division, exponentiation, square root and/or factorial, to obtain as many numbers as possible from 0, 1, 2, etcetera. (Concatenation of two or more digits is not allowed.) -- Jacques Haubrich <jhau@wsdw10.win.tue.nl>
Show solution
[ Editor: the ban on concatenation was added by Jacques Haubrich after
the first replies, so some of the early answers below use 19, 97, 99
etc. ]
[ Editor: an early list of answers, quoted by Paul Ciszek
<pciszek@nyx10.cs.du.edu> and marked "[Bobbitt]" in J Vincent's reply,
included: ]
14 = (1+(9/9))*7
15 = AAARGH!
16 = ((-1)+9)*(9-7)
15 = 19 + sqrt(9) - 7
-- Bill Taylor <mathwft@math.canterbury.ac.nz>
[Bobbitt]
> 4 = (-1)+SQRT(9)+9-7 can anyone find a way to do 4 w/o roots?
How about (19 + 9) / 7
[Bobbitt]
> 26 = 1+9+9+7
27 = (1 * sqrt(9))! + (sqrt(9) * 7)
28 = 1 + sqrt(9) + sqrt(9+7)!
29 = 19 + sqrt(9) + 7
30 = 1 + (sqrt(9)! * sqrt(9)!) - 7
31 = 1 + (sqrt(9)! + sqrt(9+7)!
32 = -1 + 9 + sqrt(9+7)!
33 = (1 * 9) + sqrt(9+7)!
34 = (1 + sqrt(9))! + sqrt(9) + 7
35 = 19 + 9 + 7 --OR-- -1 + sqrt(9)! + (sqrt(9)! + 7) (see below)
36 = -(1 * sqrt(9)!) + (sqrt(9)! * 7)
37 = -1 + sqrt(9)! + (sqrt(9)! * 7)
38 = 19 * (9 - 7) --OR-- -(1 + sqrt(9)) + (sqrt(9)! + 7) (see below)
39 = -(1 * sqrt(9)) + (sqrt(9)! * 7)
40 = 1 - sqrt(9) + (sqrt(9)! * 7)
41 = -(1 ^ 9) + (sqrt(9)! * 7)
42 = (1 ^ 9) * (sqrt(9)! * 7)
43 = (1 ^ 9) + (sqrt(9)! * 7)
44 = -1 + sqrt(9) + (sqrt(9)! * 7)
45 = (1 * sqrt(9)) + (sqrt(9)! * 7)
46 = 1 + sqrt(9) + (sqrt(9)! * 7)
47 = -1 + sqrt(9)! + (sqrt(9)! * 7)
48 = (1 * sqrt(9)!) + (sqrt(9)! * 7)
49 = 1 + sqrt(9)! + (sqrt(9)! * 7)
50 = -1 + 9 + (sqrt(9)! * 7)
51 = (1 * 9) + (sqrt(9)! * 7)
52 = 1 + 9 + (sqrt(9)! * 7)
53 = -(1 + 9) + (9 * 7)
54 = -(1 * 9) + (9 * 7)
55 = -1 + 9 + (9 * 7)
[ Editor: as written, the second forms for 35 and 38 evaluate to 18
and 9, and the line for 37 evaluates to 47 (it is the same as the line
for 47); 55 = -1 + 9 + 63 is 71 (1 - 9 + 63 = 55). ]
56 to 73: same as corresponding 35 to 52, except substitute (9 * 7) for
(sqrt(9)! * 7), up to
73 = 1 + 9 + (9 * 7)
[ Editor: "35 to 53" in the original posting; corrected by the author
in a follow-up. ]
With the digit 9 one can get 3, 6 or 9, so with 1 and 9 it's possible to
obtain everything between -10 and +10.
For 74 through 82, use 9!/7! = 72 for the last two digits:
74 = -1 + sqrt(9) + (9!/7!)
75 = (1 * sqrt(9)) + (9!/7!)
...
82 = 1 + 9 + (9!/7!)
For 87 through 107 we can just use 97
87 = -1 - 9 + 97
88 = -(1 * 9) + 97
...
107 = 1 + 9 + 97
So now all we need are 83, 84, 85 and 86 to get everything up to 100.
83 = ((1 + 9) * 9) - 7
84 = ?
85 = ?
86 = ?
-- J Vincent <jvincent@mcs.net>
> 4 = (-1)+SQRT(9)+9-7 can anyone find a way to do 4 w/o roots?
I found a way to do 4 w/o roots.
4=(-1+9)/(9-7)
-- Hiroyuki Okada <695l5019@mn.waseda.ac.jp>
84 = (1 + sqr(9)) * sqr(9) * 7
-- Bill Taylor <mathwft@math.canterbury.ac.nz>
85 = 1 + (9 + sqrt(9))*7
86 = -1 + (sqrt(9)!)!/9 + 7
-- Fred W. Helenius <fredh@ix.netcom.com>
Thanks for all your contributions and my apologies to you all since I
forgot to mention that concatenation of two or more digits is not allowed.
No despair, still most results are obtainable.
In the following list, I just write 3 for SQRT(9) and 6 for (SQRT(9))!
0 = 1*(9-9)*7
1 = 1+(9-9)*7
2 = 1+(9/9)^7
3 = -1-9/3+7
4 = (-1+3)*(9-7)
5 = (1+9)/(9-7)
6 = -1-9+9+7
7 = 1*9-9+7
8 = 1+9-9+7
9 = 1+(9/9)+7
10 = -1+9+9-7
11 = 1*9+9-7
12 = 1+9+9-7
13 = 1*9-3+7
14 = (1+9/9)*7
15 = -1+6+3+7
16 = 1^9*9+7
17 = 1^9+9+7
18 = -1+3+9+7
19 = 1+9*(9-7)
20 = 1+9+3+7
21 = 1+9*3-7
22 = 1+(9/3)*7
23 = 1+6+9+7
24 = -1+9+9+7
25 = 1*9+9+7
26 = 1+9+9+7
27 = 1*6 +3*7
28 = 1+3+(SQR(9+7))!
29 = -1+9+3*7
30 = 1*9+3*7
31 = 1+9+3*7
32 = -1-9+6*7
33 = -1*9+6*7
34 = 1-9+6*7
35 = (-1+3+3)*7
36 = -1*6+6*7
37 = 1-6+6*7
38 = -1-3+6*7
39 = -1*3+6*7
40 = 1-3+6*7
41 = -1^9+6*7
42 = (1*3+3)*7
43 = 1+(3+3)*7
44 = -1+3+6*7
45 = 1*3+6*7
46 = 1+3+6*7
47 = -1+6+6*7
48 = 1*6+6*7
49 = 1+6+6*7
50 = -1+9+6*7
51 = 1*9+6*7
52 = 1+9+6*7
53 = -1-9+9*7
54 = -1*9+9*7
55 = 1-9+9*7
56 = -1-6+9*7
57 = -1*6+9*7
58 = 1-6+9*7
59 = -1-3+9*7
60 = -1*3+9*7
61 = 1-3+9*7
62 = -1^9+9*7
63 = (1*3+6)*7
64 = 1^9+9*7
65 = -1+3+9*7
66 = 1*3+9*7
67 = 1+3+9*7
68 = -1+6+9*7
69 = 1*6+9*7
70 = 1+6+9*7
71 = -1+9+9*7
72 = 1*9+9*7
73 = -1+9*9-7
74 = 1*9*9-7
75 = 1+9*9-7
76 = 1+3+9!/7!
77 = -1+6*(6+7)
78 = 1*6*(6+7)
79 = 1+6*(6+7)
80 = (1+6)!/(9*7)
81 = 1*3^(-3+7)
82 = 1+3^(-3+7)
83 = (1+9)*9-7
84 = (1+3)*3*7
85 = 1+(9+3)*7
86 = -1+6!/9+7 [Editor: "1+6!/9+7" (= 88) in the original]
87 = -1+9*9+7
88 = 1*9*9+7
89 = 1+9*9+7
90 = 1*9*(3+7)
91 = 1+9*(3+7)
92 =
93 =
94 =
95 = -1+6*(9+7)
96 = 1*6*(9+7)
97 = (1+9)*9+7
98 = (-1+6+9)*7
99 =
100 = (1+9)*(3+7)
Only 4 cases (below 100) are still missing. Who is able to find one or more
of these, or is there a real PROOF that these are impossible?
Are there improvements, especially solutions without or with lesser use of
SQRT(9) and/or SQRT(9)! ?
Are there nicer solutions (you decide upon what you consider nice!)
-- Jacques Haubrich <jhau@win.tue.nl>
99 = (-1+6)!-3*7
-- Fred W. Helenius <fredh@ix.netcom.com>
(the same answer was posted by Dean Hickerson <dean@ucdmath.ucdavis.edu>)
92 = 1+SQR(9)+3+7
93 = -1+SQR(9)+6+7
94 = (1*SQR(9))+6+7
Hmm.. I may have replied too soon - SQR() is probably not allowed.
-- Ajit Thyagarajan <ajit@ren.eecis.udel.edu>
[ Editor: here SQR(9) means 9 squared, 81. ]
0 = 1*(9-9)*7
1 = 1+(9-9)*7
2 = 1^9*(9-7)
3 = 1^9+9-7
4 = (-1+9)/(9-7)
5 = (1+9)/(9-7)
6 = -1+9-9+7
7 = 1*9-9+7
8 = 1+9-9+7
9 = 1+9/9+7
10 = -1+9+9-7
11 = 1*9+9-7
12 = 1+9+9-7
13 = 1-9+sqrt(9)*7
14 = (1+9/9)*7
15 = -1^9+9+7
16 = (-1+9)*(9-7)
17 = -1+9*(9-7)
18 = 1*9*(9-7)
19 = 1+9*(9-7)
20 = (1+9)*(9-7)
21 = 1^9*sqrt(9)*7
22 = 1^9+sqrt(9)*7
23 = (1+9)*sqrt(9)-7
24 = -1+9+9+7
25 = 1*9+9+7
26 = 1+9+9+7
27 = 1*(sqrt(9))!+sqrt(9)*7
28 = (1+9/sqrt(9))*7
29 = -1+9+sqrt(9)*7
30 = 1*9+sqrt(9)*7
31 = 1+9+sqrt(9)*7
32 = (-1+9)*(-sqrt(9)+7)
33 = -1+sqrt(9)^sqrt(9)+7
34 = 1*sqrt(9)^sqrt(9)+7
35 = (-1+sqrt(9)+sqrt(9))*7
36 = 1*9*(-sqrt(9)+7)
37 = (1+9)*sqrt(9)+7
38 = (-1+(sqrt(9))!)*9-7
39 = 1*sqrt(9)*((sqrt(9))!+7)
40 = 1+sqrt(9)*((sqrt(9))!+7)
41 = -1^9+(sqrt(9))!*7
42 = 1*(sqrt(9)+sqrt(9))*7
43 = 1+(sqrt(9)+sqrt(9))*7
44 = 1+(sqrt(9))!*(sqrt(9))!+7
45 = 1*sqrt(9)+(sqrt(9))!*7
46 = 1+sqrt(9)+(sqrt(9))!*7
47 = -1+sqrt(9)*(9+7)
48 = 1*sqrt(9)*(9+7)
49 = (1-sqrt(9)+9)*7
50 = (-1+(sqrt(9))!)*(sqrt(9)+7)
51 = 1*9+(sqrt(9))!*7
52 = (-1+(sqrt(9))!)*9+7
53 = -1-9+9*7
54 = -1*9+9*7
55 = 1-9+9*7
56 = (-1+sqrt(9)*sqrt(9))*7
57 = -1*(sqrt(9))!+9*7
58 = 1-(sqrt(9))!+9*7
59 = -1-sqrt(9)+9*7
60 = -1*sqrt(9)+9*7
61 = 1-sqrt(9)+9*7
62 = -1^9+9*7
63 = 1^9*9*7
64 = 1^9+9*7
65 = -1+sqrt(9)+9*7
66 = 1*sqrt(9)+9*7
67 = 1+sqrt(9)+9*7
68 = -1+(sqrt(9))!+9*7
69 = 1*(sqrt(9))!+9*7
70 = (1^9+9)*7
71 = -1+9+9*7
72 = 1*9+9*7
73 = -1+9*9-7
74 = 1*9*9-7
75 = 1+9*9-7
76 = 1+sqrt(9)+9!/7!
77 = (-1+sqrt(9)+9)*7
78 = 1*(sqrt(9))!*((sqrt(9))!+7)
79 = (-1+9)*9+7
80 = -1+9+9!/7!
81 = 1*9+9!/7!
82 = 1+9+9!/7!
83 = (1+9)*9-7
84 = (1*sqrt(9)+9)*7
85 = 1+(sqrt(9)+9)*7
86 = -1+((sqrt(9))!)!/9+7
87 = -1+9*9+7
88 = 1*9*9+7
89 = 1+9*9+7
90 = 1*9*(sqrt(9)+7)
91 = 1+9*(sqrt(9)+7)
92 = -1-sqrt(9)-9+7!!
93 = -1*sqrt(9)-9+7!!
94 = 1-sqrt(9)-9+7!!
95 = -1+(sqrt(9))!*(9+7)
96 = 1*(sqrt(9))!*(9+7)
97 = (1+9)*9+7
98 = (-1+9+(sqrt(9))!)*7
99 = (-1+(sqrt(9))!)!-sqrt(9)*7
100 = (1+9)^(9-7)
!! is the double-factorial function - (2*n-1)!! = 1*3*...*(2*n-1)
-- Ilan Mayer <ilmayer@aol.com>
Try this PASCAL program, well, you have to implement power (x^y) for
some entries.
[ Editor: in the program K(x) is the rounded square root, F(x) is x!
and F2(x) is the double factorial x!!. The number each line produces
is in braces at the right. ]
{----------------------------------AJ avgust 1996--------------------------}
function k(x:integer):integer;
begin k:=round( sqrt(x) ); end;
function f(x:integer):integer; { X! FACTORIAL}
begin if x<=0 then f:=1 else f:=x*f(x-1); end;
function f2(x:integer):integer; { X!! DOUBLE FACTORIAL }
begin if x<=1 then f2:=1 else f2:=x*f2(x-2); end;
begin
writeln('1997');
writeln(' 1*(9-9)*7 = ', 1*(9-9)*7 ); { 0 }
writeln(' 1+(9-9)*7 = ', 1+(9-9)*7 ); { 1 }
writeln(' 1*K(9*9)-7 = ', 1*K(9*9)-7 ); { 2 }
writeln(' 19-9-7 = ', 19-9-7 ); { 3 }
writeln(' (19+9)/7 = ', (19+9) div 7 ); { 4 }
writeln(' (1-9)/(-9+7) = ', (1-9) div (-9+7) ,'*' ); { 4*}
writeln(' -1-9/9+7 = ',-1-9 div 9+7 ); { 5 }
writeln(' -1+9-9+7 = ', -1+9-9+7 ); { 6 }
writeln(' 1*9-9+7 = ', 1*9-9+7 ); { 7 }
writeln(' 1+9-9+7 = ', 1+9-9+7 ); { 8 }
writeln(' 1+9/9+7 = ', 1+9 div 9+7 ); { 9 }
writeln(' -1+9+9-7 = ', -1+9+9-7 ); {10 }
writeln(' 1*9+9-7 = ', 1*9+9-7 ); {11 }
writeln(' 1+9+9-7 = ', 1+9+9-7 ); {12 }
writeln(' 1*K(9)+K(9)+7 = ', 1*K(9)+K(9)+7 ); {13 }
writeln(' (-1+99)/7 = ', (-1+99) div 7 ); {14 }
writeln(' -1+K(9*9)+7 = ',-1+K(9*9)+7 ); {15 }
writeln(' (-1+9)*(9-7) = ', (-1+9)*(9-7) ); {16 }
writeln(' -1+9*(9-7) = ', -1+9*(9-7) ); {17 }
writeln(' 1*9*(9-7) = ', 1*9*(9-7) ); {18 }
writeln(' 1+9*(9-7) = ', 1+9*(9-7) ); {19 }
writeln(' (+1+9)*(9-7) = ', (+1+9)*(9-7) ); {20 }
writeln(' 19+9-7 = ', 19+9-7 ); {21 }
writeln(' F(1+K(9))-9+7 = ', F(1+K(9))-9+7 ); {22 }
writeln(' 19-K(9)+7 = ', 19-K(9)+7 ); {23 }
writeln(' -1+9+9+7 = ', -1+9+9+7 ); {24 }
writeln(' 1*9+9+7 = ', 1*9+9+7 ); {25 }
writeln(' 1+9+9+7 = ', 1+9+9+7 ); {26 }
writeln('1*F(K(9))+K(9)*7) = ', 1*F(K(9))+K(9)*7 ); {27 }
writeln('-1+F(K(9))*F(K(9))-7 = ', -1+F(K(9))*F(K(9))-7 ); {28 }
writeln(' 19+K(9)+7 = ', 19+K(9)+7 ); {29 }
writeln(' 1*9+K(9)*7 = ', 1*9+K(9)*7 ); {30 }
writeln(' 1+9+K(9)*7 = ', 1+9+K(9)*7 ); {31 }
writeln(' -1-9+F(K(9))*7 = ', -1-9+F(K(9))*7 ); {32 }
writeln(' -1+9*K(9)+7 = ', -1+9*K(9)+7 ); {33 }
writeln(' 1*9*K(9)+7 = ', 1*9*K(9)+7 ); {34 }
writeln(' 19+9+7 = ', 19+9+7 ); {35 }
writeln('-1*F(K(9))+F(K(9))*7) = ', -1*F(K(9))+F(K(9))*7 ); {36 }
writeln(' 1-F(K(9))+F(K(9))*7) = ', 1-F(K(9))+F(K(9))*7 ); {37 }
writeln(' 19*(9-7) = ', 19*(9-7) ); {38 }
writeln(' -1*K(9)+F(K(9))*7) = ', -1*K(9)+F(K(9))*7 ); {39 }
writeln(' 19+K(9)*7 = ', 19+K(9)*7 ); {40 }
writeln('-1+(K(9)+K(9))*7 = ', -1+(K(9)+K(9))*7 ); {41 }
writeln(' 1*(K(9)+K(9))*7 = ', 1*(K(9)+K(9))*7 ); {42 }
writeln(' 1+(K(9)+K(9))*7 = ', 1+(K(9)+K(9))*7 ); {43 }
writeln(' -1+K(9)+F(K(9))*7) = ', -1+K(9)+F(K(9))*7 ); {44 }
writeln(' 1*K(9)+F(K(9))*7) = ', 1*K(9)+F(K(9))*7 ); {45 }
writeln(' 1+K(9)+F(K(9))*7) = ', 1+K(9)+F(K(9))*7 ); {46 }
writeln(' -1+F(K(9))+F(K(9))*7) = ', -1+F(K(9))+F(K(9))*7 ); {47 }
writeln(' 1*F(K(9))+F(K(9))*7) = ', 1*F(K(9))+F(K(9))*7 ); {48 }
writeln(' (1+K(9)+K(9))*7 = ', (1+K(9)+K(9))*7 ); {49 }
writeln(' 19*(K(9)-7 = ', 19*K(9)-7 ); {50 }
writeln(' 1*9+F(K(9))*7 = ', 1*9+F(K(9))*7 ); {51 }
writeln(' 1+9+F(K(9))*7 = ', 1+9+F(K(9))*7 ); {52 }
writeln(' -1-9+9*7 = ', -1-9+9*7 ); {53 }
writeln(' -1*9+9*7 = ', -1*9+9*7 ); {54 }
writeln(' +1-9+9*7 = ', +1-9+9*7 ); {55 }
writeln(' -1-F(K(9))+9*7 = ', -1-F(K(9))+9*7 ); {56 }
writeln(' -1*F(K(9))+9*7 = ', -1*F(K(9))+9*7 ); {57 }
writeln(' +1-F(K(9))+9*7 = ', 1-F(K(9))+9*7 ); {58 }
writeln(' -1-K(9)+9*7 = ', -1-K(9)+9*7 ); {59 }
writeln(' -1*K(9)+9*7 = ', -1*K(9)+9*7 ); {60 }
writeln(' ( 1*9)*F(K(9))+7) = ', ( 1*9)*F(K(9))+7 ); {61 }
writeln(' 1+9*F(K(9))+7 = ', 1+9*F(K(9))+7 ); {62 }
writeln(' 1^9*9*7 = ', 1*9*7 ); {63 }
{ [Editor: the string reads "1^9*9-7" in the original] }
writeln(' 19*(K(9)+7 = ', 19*K(9)+7 ); {64 }
writeln(' F(1+K(9))*K(9)-7 = ', F(1+K(9))*K(9)-7 ); {65 }
writeln(' 1*K(9)+9*7 = ', 1*K(9)+9*7 ); {66 }
writeln(' +1+K(9)+9*7 = ', +1+K(9)+9*7 ); {67 }
writeln(' -1+F(K(9))+9*7 = ', -1+F(K(9))+9*7 ); {68 }
writeln(' 1*F(K(9))+9*7 = ', 1*F(K(9))+9*7 ); {69 }
writeln(' K(1+99)*7 = ', K(1+99)*7 ); {70 }
{ [Editor: the string reads "K(199)*7" in the original] }
writeln(' -1+K(9)*F(-(K(9))+7) = ', -1+K(9)*F(-(K(9))+7) ); {71 }
writeln(' 1*K(9)*F(-(K(9))+7) = ', 1*K(9)*F(-(K(9))+7) ); {72 }
writeln(' -1+9*9-7 = ', -1+9*9-7 ); {73 }
writeln(' 1*9*9-7 = ', 1*9*9-7 ); {74 }
writeln(' 1+9*9-7 = ', 1+9*9-7 ); {75 }
writeln(' 19*(-K(9)+7) = ', 19*(-K(9)+7) ); {76 }
writeln(' (-1+9+K(9))*7 = ', (-1+9+K(9))*7 ); {77 }
writeln(' -19+97 = ', -19+97 ); {78 }
writeln(' (-1+9)*9+7 = ', (-1+9)*9+7 ); {79 }
writeln(' (-1+9)*(K(9)+7) = ', (-1+9)*(K(9)+7) ); {80 }
writeln(' 1*9^(9-7) = ', 1*{9^}(9-7) ); {81 }
writeln(' +1+9^(9-7) = ', +1+{9^}(9-7) ); {82 }
writeln(' -1+(K(9)+9)*7 = ',-1+(K(9)+9)*7 ); {83 }
writeln(' (1*K(9)+9)*7 = ', (1*K(9)+9)*7 ); {84 }
writeln(' 1+(K(9)+9)*7 = ', 1+(K(9)+9)*7 ); {85 }
writeln(' -1-9-9+F2(7) = ', -1-9-9+F2(7) ); {86 }
writeln(' -1+9*9+7 = ', -1+9*9+7 ); {87 }
writeln(' 1*9*9+7 = ', 1*9*9+7 ); {88 }
writeln(' 1+9*9+7 = ', 1+9*9+7 ); {89 }
writeln(' -1-F(K(9))+97 = ', -1-F(K(9))+97 ); {90 }
writeln(' -1+99-7 = ', -1+99-7 ); {91 }
writeln(' 1*99-7 = ', 1*99-7 ); {92 }
writeln(' 1+99-7 = ', 1+99-7 ); {93 }
writeln(' -1*K(9)+97 = ', -1*K(9)+97 ); {94 }
writeln(' 1-K(9)+97 = ', 1-K(9)+97 ); {95 }
writeln(' 1*F(K(9))*(9+7) = ', 1*F(K(9))*(9+7) ); {96 }
writeln(' (1+9)*9+7 = ', (1+9)*9+7 ); {97 }
writeln(' (-1+F(K(9))+9)*7 = ', (-1+F(K(9))+9)*7 ); {98 }
writeln(' -1+K(9)+97 = ', -1+K(9)+97 ); {99 }
writeln(' 1*K(9)+97 = ', 1*K(9)+97 ); {100}
writeln(' 1+K(9)+97 = ', 1+K(9)+97 ); {101}
writeln(' -1+F(K(9))+97 = ', -1+F(K(9))+97 ); {102}
writeln(' 1*F(K(9))+97 = ', 1*F(K(9))+97 ); {103}
writeln(' +1+F(K(9))+97 = ', +1+F(K(9))+97 ); {104}
writeln(' -1+99+7 = ', -1+99+7 ); {105}
writeln(' 1*99+7 = ', 1*99+7 ); {106}
writeln(' +1+99+7 = ', +1+99+7 ); {107}
writeln(' = ', +1+9 div 9+F2(7) ); {108}
{ [Editor: 1 + 9/9 + 7!! = 1 + 1 + 105 = 107, not 108] }
writeln(' (1+F(K(9))+9)*7 = ', (1+F(K(9))+9)*7 ); {112}
writeln(' 19+97 = ', 19+97 ); {116}
writeln(' (-1+9+9)*7 = ', (-1+9+9)*7 ); {119}
writeln(' F(1+K(9))+97 = ', F(1+K(9))+97 ); {121}
writeln(' (1*9+9)*7 = ', (1*9+9)*7 ); {126}
writeln(' (1+9/9)^7 = ', (1+9/9){^7} ); {128}
writeln(' ( 19+K(9))*7 = ', ( 19+K(9))*7 ); {154}
writeln(' (-1+9)*(K(9))*7 = ', (-1+9)*(K(9))*7 ); {168}
writeln(' ( 19+F(K(9)))*7 = ', ( 19+F(K(9)))*7 ); {175}
writeln(' (-1+9*K(9))*7 = ', (-1+9*K(9))*7 ); {182}
writeln(' (1*9*K(9))*7 = ', (1*9*K(9))*7 ); {189}
writeln(' 199-7 = ', 199-7 ); {192}
writeln(' (19+9)*7 = ', (19+9)*7 ); {196}
writeln(' 199+7 = ', 199+7 ); {206}
writeln(' 19^(9-7) = ', {19^}(9-7) ); {361}
readln;
end.
-- AndreJ Jakobcic <AndreJ.Jakobcic@guest.arnes.si>