The Museum of HP Calculators

An XOR Game for the HP-41

This program is supplied without representation or warranty of any kind. Jean-Marc Baillard and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Overview

-The purpose of this game is to change the display from "----------" ( ten "-" characters ) into "**********" ( ten "*" characters )
-Pressing a numeric key ( from "1" to "9" ) followed by R/S changes some "-" into "*" and some "*" into "-"
-The transformation is reversible.
-Actually, each operation is a logical eXclusive OR ( "-" beeing 0 and "*" beeing 1 ). The result is placed in the alpha register and displayed.
-If you find a solution, the HP-41 displays "**********" , you hear a BEEP and your number of tries is in registers X and R12.
-There is always ( at least ) one 4 keystroke solution which is stored in register R11.
-Finding a solution without pen and paper is quite a feat!

-The first "XOR" program uses 103 data registers.
-In case you have not enough room to execute SIZE 103 , "XOR2" is then listed ( it is a little bit slower but only 16 registers are used )
-Finally, "XOR3" is an easier version which displays 6 character strings , using only 5 numeric keys ( from "1" to "5" ) , with a solution in 3 keystrokes.

Program#1

Data Registers: • R00 = random numbers ( this register is to be initialized before executing "XOR" )
R01 to R10 correspond to the 10 displayed characters R13 thru R22    correspond to the "1" key
R11 = one solution       -----------------------------------------
R12 = the score = the number of guesses    R93 thru R102 correspond to the "9" key
Flag: F10
Subroutine: /

001 LBL "XOR"
002 9
003 LBL 00
004 STO IND X
005 DSE X
006 GTO 00
007 STO 11
008 4
009 STO 12
010 9
011 LBL 01
012 STO Y
013 RCL 00 All these programs use the same random number generator: RCL 00 R-D FRC STO 00
014 R-D
015 FRC
016 STO 00
017 *
018 10
019 ST* 11
020 SIGN
021 +
022 RCL IND X
023 ST+ 11
024 X<> IND Z
025 STO IND Y
026 RDN
027 SIGN
028 -
029 DSE 12
030 GTO 01
031 102.012
032 STO 02
033 LBL 02
034 RCL 00
035 R-D
036 FRC
037 STO 00
038 ST+ X
039 INT
040 STO IND 02
041 DSE 02
042 GTO 02
043 10
044 STO 01
045 ST* 06
046 ST* 07
047 ST* 08
048 ST* 09
049 12
050 ST+ 06
051 ST+ 07
052 ST+ 08
053 ST+ 09
054 LBL 03
055 SIGN
056 RCL IND 06
057 +
058 RCL IND 07
059 +
060 RCL IND 08
061 +
062 2
063 MOD
064 STO IND 09
065 DSE 06
066 DSE 07
067 DSE 08
068 DSE 09
069 DSE 01
070 GTO 03
071 2.01 If you don't have an HP-41CX, replace lines 71-72 by CLX STO 02 STO 03 STO 04 STO 05 STO 06
072 CLRGX    STO 07 STO 08 STO 09 STO 10
073 LBL 04
074 SF 10
075 10
076 " " ( one space )
077 LBL 05
078 RCL IND X
079 X=0?
080 CF 10
081 X=0?
082 "~-" ( I mean: append - )
083 X#0?
084 "~*" ( append * )
085 X<>Y
086 DSE X
087 GTO 05
088 AVIEW
089 FS?C 10
090 GTO 07
091 STOP
092 AVIEW
093 10
094 *
095 12
096 +
097 10
098 LBL 06
099 RCL IND Y
100 RCL IND Y
101 +
102 2
103 MOD
104 STO IND Y
105 DSE Z
106 RDN
107 DSE X
108 GTO 06
109 SIGN
110 ST+ 12
111 GTO 04
112 LBL 07
113 RCL 12
114 BEEP
115 END

( 193 bytes / SIZE 103 )

Example: With 0.1883185174 STO 00

XEQ "XOR" 49 seconds later ( t₀ ) , the program stops and the HP-41 displays "----------"

Press ( for instance ) 1 R/S the previous string is displayed again and 7 seconds later ( t₁) , you'll see "-*-*--***-"
2 R/S >>>> "**--*-****"
3 R/S >>>> "---**-*---"
4 R/S >>>> "----**--*-"
5 R/S >>>> "-*****--*-"
6 R/S >>>> "---*****--"
7 R/S >>>> "----*---*-" from which we can gradually deduce the following informations:

-The 1st character is changed by 2 ; 3
-The 2nd ----------------------- 1 ; 3 ; 5 ; 6
-The 3rd ----------------------- 5 ; 6
-The 4th ----------------------- 1 ; 2 ; 3 ; 4 ; 5 ; 7
-The 5th ----------------------- 2
-The 6th ----------------------- 4 ; 7
-The 7th ----------------------- 1 ; 4 ; 6 ; 7
-The 8th ----------------------- 1 ; 3 ; 6 ; 7
-The 9th ----------------------- 1 ; 3 ; 4 ; 6 ; 7
-The 10th ---------------------- 2 ; 3

-We'll have a solution if all the 10 characters are changed an odd number of times, therefore we can try to "switch off" 4 ; 3 ; 1 ; 6:

4 R/S >>>> "---****---"
3 R/S >>>> "**--******"
1 R/S >>>> "*--***---*"
6 R/S >>>> "**********" ( BEEP ) and X = R12 = 11 = the number of our guesses. We have found one solution = 2-5-7

-In this example, we didn't have to press 8 or 9 but the HP-41 gives another solution in register R11 = 8-3-5-9.

Note: -If you have an HP-41CX, lines 92-93 may be replaced with the 4 lines: 99 GETKEYX 48 -
and you'll only have to press the numeric key ( without R/S ).

Program#2

Data Registers: • R00 = random numbers ( this register is to be initialized before executing "XOR2" )
R01 to R09 correspond to the 9 numeric keys R10 corresponds to the 10 displayed characters R13 to R15: temp.
R11 = one solution R12 = the score
Flag: F10
Subroutine: /

001 LBL "XOR2"
002 9
003 LBL 00
004 STO IND X
005 DSE X
006 GTO 00
007 STO 11
008 4
009 STO 10
010 15
011 9
012 LBL 01
013 RCL 00
014 R-D
015 FRC
016 STO 00
017 RCL Y
018 *
019 10
020 ST* 11
021 SIGN
022 +
023 RCL IND X
024 ST+ 11
025 STO IND T
026 X<> IND Z
027 STO IND Y
028 RDN
029 SIGN
030 ST- Z
031 -
032 DSE 10
033 GTO 01
034 9
035 STO 10
036 LBL 02
037 10
038 ENTER^
039 CLX
040 LBL 03
041 10
042 *
043 RCL 00
044 R-D
045 FRC
046 STO 00
047 ST+ X
048 INT
049 +
050 DSE Y
051 GTO 03
052 STO IND 10
053 DSE 10
054 GTO 02
055 RCL IND 12
056 RCL IND 13
057 RCL IND 14
058 +
059 +
060 10
061 STO 10
062 SIGN
063 STO 12
064 CLX
065 STO IND 15
066 X<>Y
067 LBL 04
068 ENTER^
069 ENTER^
070 SIGN
071 +
072 2
073 MOD
074 RCL 12
075 *
076 ST+ IND 15
077 CLX
078 10
079 ST* 12
080 /
081 INT
082 DSE 10
083 GTO 04
084 CLX
085 STO 12
086 LBL 05
087 SF 10
088 10
089 " " ( one space )
090 RCL 10
091 LBL 06
092 ENTER^
093 ENTER^
094 2
095 MOD
096 X=0?
097 CF 10
098 X=0?
099 "~-" ( append - )
100 X#0?
101 "~*" ( append * )
102 CLX
103 10
104 /
105 INT
106 DSE Y
107 GTO 06
108 AVIEW
109 FS?C 10
110 GTO 08
111 STOP
112 AVIEW
113 10
114 STO 13
115 SIGN
116 STO 14
117 CLX
118 X<> 10
119 RCL IND Y
120 +
121 LBL 07
122 STO Y
123 2
124 MOD
125 RCL 14
126 *
127 ST+ 10
128 CLX
129 10
130 ST* 14
131 /
132 INT
133 DSE 13
134 GTO 07
135 SIGN
136 ST+ 12
137 GTO 05
138 LBL 08
139 RCL 12
140 BEEP
141 END

( 208 bytes / SIZE 016 )

-This program is slower than "XOR": t₀ = 62 seconds ; t₁ = 11 seconds.
-The 10 characters are displayed in the reversed order but this doesn't change the strategy.

Program#3

Data Registers: • R00 = random numbers ( this register is to be initialized before executing "XOR3" )
R01 to R06 correspond to the 6 displayed characters R09 thru R14    correspond to the "1" key
R07 = one solution       -----------------------------------------
R08 = the score    R33 thru R38 correspond to the "5" key
Flag: F10
Subroutine: /

001 LBL "XOR3"
002 5
003 LBL 00
004 STO IND X
005 DSE X
006 GTO 00
007 STO 07
008 3
009 STO 08
010 5
011 LBL 01
012 STO Y
013 RCL 00
014 R-D
015 FRC
016 STO 00
017 *
018 10
019 ST* 07
020 SIGN
021 +
022 RCL IND X
023 ST+ 07
024 X<> IND Z
025 STO IND Y
026 RDN
027 SIGN
028 -
029 DSE 08
030 GTO 01
031 38.008
032 STO 02
033 LBL 02
034 RCL 00
035 R-D
036 FRC
037 STO 00
038 ST+ X
039 INT
040 STO IND 02
041 DSE 02
042 GTO 02
043 6
044 STO 01
045 ST* 03
046 ST* 04
047 ST* 05
048 8
049 ST+ 03
050 ST+ 04
051 ST+ 05
052 LBL 03
053 SIGN
054 RCL IND 03
055 +
056 RCL IND 04
057 +
058 2
059 MOD
060 STO IND 05
061 DSE 03
062 DSE 04
063 DSE 05
064 DSE 01
065 GTO 03
066 CLX
067 STO 02
068 STO 03
069 STO 04
070 STO 05
071 STO 06
072 LBL 04
073 SF 10
074 6
075 " " ( one space )
076 LBL 05
077 RCL IND X
078 X=0?
079 CF 10
080 X=0?
081 "~-" ( append - )
082 X#0?
083 "~*" ( append * )
084 X<>Y
085 DSE X
086 GTO 05
087 AVIEW
088 FS?C 10
089 GTO 07
090 STOP
091 AVIEW
092 6
093 *
094 8
095 +
096 6
097 LBL 06
098 RCL IND Y
099 RCL IND Y
100 +
101 2
102 MOD
103 STO IND Y
104 DSE Z
105 RDN
106 DSE X
107 GTO 06
108 SIGN
109 ST+ 08
110 GTO 04
111 LBL 07
112 RCL 08
113 BEEP
114 END

( 178 bytes / SIZE 039 )

Example: With 1 STO 00

XEQ "XOR3" , 20 seconds later, the HP-41 displays "------"

1 R/S >>>> ( 5 seconds later ) "-*-**-"
2 R/S >>>> "---**-"
3 R/S >>>> "*-**--"
4 R/S >>>> "-*-*-*"
5 R/S >>>> "*--**-" Similar arguments suggest to switch off 3 and 5

3 R/S >>>> "--**--"
5 R/S >>>> "******" ( BEEP ) and X = R08 = 7 guesses.

-We have found the solution 1-2-4 which is confirmed by register R07 = 241.

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