The Museum of HP Calculators


Le Compte est Bon for the HP-41

This program is Copyright © 2007 by Jean-Marc Baillard and is used here by permission.

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
 

-"Le compte est bon" is a French TV game:
-6 numbers ( n1 , n2 , n3 , n4 , n5 , n6  ) are choosen at random among the 24 integers:

  1 - 1 - 2 - 2 - 3 - 3 - 4 - 4 - 5 - 5 - 6 - 6 - 7 - 7 - 8 - 8 - 9 - 9 - 10 - 10 - 25 - 50 - 75 - 100  ( for instance  1 - 9 - 8 - 4 - 3 - 100 )

 and you have to find another random number N ( between 100 and 999 inclusive )  , say  N = 629 , using the 6 numbers above ( or less )
 and the 4 basic operations: addition, subtraction, multiplication, division.

-For example, one solution of the above problem is:

    100 - 1 = 99
    99 / 3 = 33
    33 + 4 = 37
    9 + 8 = 17
    37 * 17 = 629

-A solution has - at most - 5 operations and the same number cannot be used several times.
-More exactly, you can use "ni" twice or less if there are 2 "ni"s
               and   ---------------- once ---------------  is  1 "ni"

-The following program can help you to find one or several solution(s) to this problem.
 

Program Listing
 

Data Registers:      R01 = n1     R02 = n2  ..........     R06 = n6       R07 = N     ( these 7 registers are to be initialized before executing "LCEB" )
                                   R00 & R08 thru R17: temp

Flags:  F05-F06-F07
Subroutines: /
 

  01  LBL "LCEB"
  02  6
  03  STO 12
  04  5
  05  STO 13
  06  STO 16
  07  4
  08  STO 14
  09  STO 17
  10  3
  11  STO 00
  12  STO 15
  13  LBL 01                           Lines 01 to 39 and 127 to 356 search a solution where the result of an operation is immediately used in the next one.
  14  RCL 07                          If - at this step - no solution is found, lines 40 thru 124 add a few other combinations.
  15  RCL 07
  16  RCL 01
  17  /
  18  STO 08
  19  CF 05
  20  X#Y?
  21  FRC
  22  X=0?
  23  XEQ 02
  24  RCL 07
  25  RCL 01
  26  -
  27  STO 08
  28  SF 05
  29  XEQ 02
  30  RCL 07
  31  RCL 01
  32  +
  33  STO 08
  34  XEQ 02
  35  RCL 01
  36  X<> IND 12
  37  STO 01
  38  DSE 12
  39  GTO 01
  40  6.001
  41  STO 12
  42  STO 13
  43  LBL 12
  44  RCL 07
  45  RCL 01
  46  RCL 02
  47  +
  48  STO 08
  49  /
  50  STO 09
  51  CF 06
  52  FRC
  53  X=0?
  54  XEQ 03
  55  RCL 07
  56  RCL 07
  57  RCL 01
  58  RCL 02
  59  X=Y?
  60  GTO 00
  61  -
  62  ABS
  63  STO 08
  64  /
  65  STO 09
  66  X#Y?
  67  FRC
  68  X=0?
  69  XEQ 03
  70  LBL 00
  71  RCL 01
  72  RCL 02
  73  X<Y?
  74  X<>Y
  75  STO Z
  76  *
  77  X=Y?
  78  GTO 00
  79  STO 08
  80  RCL 07
  81  -
  82  ABS
  83  STO 09
  84  SF 06
  85  XEQ 03
  86  RCL 07
  87  RCL 08
  88  +
  89  STO 09
  90  XEQ 03
  91  RCL 07
  92  RCL 01
  93  RCL 02
  94  X>Y?
  95  X<>Y
  96  /
  97  STO 08
  98  -
  99  STO 09
100  FRC
101  X#0?
102  GTO 00
103  XEQ 03
104  RCL 07
105  RCL 08
106  +
107  STO 09
108  XEQ 03
109  LBL 00
110  RCL 02
111  X<> IND 13
112  STO 02
113  DSE 13
114  GTO 12
115  RCL 12
116  INT
117  2
118  -
119  ST+ 13
120  RCL 01
121  X<> IND 12
122  STO 01
123  DSE 12
124  GTO 12
125  "Nb NOT FOUND"
126  PROMPT
127  LBL 02
128  RCL 02
129  RCL 08
130  X=Y?
131  GTO 10
132  X<Y?
133  X<>Y
134  STO Z
135  X<>Y
136  /
137  STO 09
138  CF 06
139  X#Y?
140  FRC                             lines 132 to 141 actually uses  sup(a,b)/inf(a,b)  instead of  a/b  ( thus, more solutions may be found )
141  X=0?                            and they avoid the divisions by 1
142  XEQ 03
143  FS? 05
144  GTO 00
145  RCL 08
146  RCL 02
147  -
148  ABS                             likewise, calculating  | a - b |  produces more solutions than  a - b
149  STO 09
150  SF 06
151  XEQ 03
152  RCL 08
153  RCL 02
154  +
155  STO 09
156  XEQ 03
157  LBL 00
158  RCL 02
159  X<> 03
160  X<> 04
161  X<> 05
162  X<> 06
163  STO 02
164  DSE 13
165  GTO 12
166  RCL 16
167  STO 13
168  RTN
169  LBL 03
170  RCL 03
171  RCL 09
172  X=Y?
173  GTO 09
174  X<Y?
175  X<>Y
176  STO Z
177  X<>Y
178  /
179  STO 10
180  CF 07
181  X#Y?
182  FRC
183  X=0?
184  XEQ 04
185  FS? 06
186  GTO 00
187  RCL 09
188  RCL 03
189  -
190  ABS
191  STO 10
192  SF 07
193  XEQ 04
194  RCL 09
195  RCL 03
196  +
197  STO 10
198  XEQ 04
199  LBL 00
200  RCL 03
201  X<> 04
202  X<> 05
203  X<> 06
204  STO 03
205  DSE 14
206  GTO 03
207  RCL 17
208  STO 14
209  RTN
210  LBL 04
211  RCL 04
212  RCL 10
213  X=Y?
214  GTO 08
215  X>Y?
216  X<>Y
217  ENTER^
218  SIGN
219  X=Y?
220  GTO 00                              division & multiplication by 1 are skipped
221  RDN
222  /
223  STO 11
224  FRC
225  X=0?
226  XEQ 05
227  RCL 04
228  RCL 10
229  *
230  STO 11
231  XEQ 05
232  LBL 00
233  FS? 07
234  GTO 00
235  RCL 10
236  RCL 04
237  -
238  ABS
239  STO 11
240  XEQ 05
241  RCL 04
242  RCL 10
243  +
244  STO 11
245  XEQ 05
246  LBL 00
247  RCL 04
248  X<> 05
249  X<> 06
250  STO 04
251  DSE 15
252  GTO 04
253  RCL 00
254  STO 15
255  RTN
256  LBL 05
257  RCL 06
258  RCL 11
259  X=Y?
260  GTO 07
261  RCL 05
262  -
263  X=0?
264  GTO 07
265  ABS
266  RCL 06
267  X=Y?
268  GTO 06
269  RCL 11
270  RCL 05
271  +
272  X=Y?
273  GTO 06
274  RCL 11
275  RCL 05
276  X>Y?
277  X<>Y
278  /
279  RCL 06
280  X=Y?
281  GTO 06
282  RCL 11
283  RCL 05
284  *
285  X#Y?
286  RTN
287  LBL 06
288  RCL 11
289  RCL 05
290  RCL 06
291  XEQ 00
292  LBL 07
293  RCL 10
294  RCL 04
295  RCL 11
296  XEQ 00
297  LBL 08
298  RCL 09
299  RCL 03
300  RCL 10
301  XEQ 00
302  LBL 09
303  RCL 12
304  FRC
305  X#0?
306  GTO 11
307  RCL 08
308  RCL 02
309  RCL 09
310  XEQ 00
311  LBL 10
312  RCL 07
313  RCL 01
314  RCL 08
315  GTO 00
316  LBL 11
317  RCL 08
318  RCL 01
319  RCL 02
320  XEQ 00
321  RCL 07
322  RCL 08
323  RCL 09
324  LBL 00
325  FIX 0
326  CF 29
327  X<Y?
328  X<>Y
329  STO T
330  X<>Y
331  CLA
332  ARCL Y
333  +
334  X=Y?
335  "~+"                  append  +
336  X<> T
337  LASTX
338  -
339  X=Y?
340  "~-"                  append  -
341  X<> T
342  LASTX
343  ST/ T
344  *
345  X=Y?
346  "~*"                 append  *
347  X<> T
348  X=Y?
349  "~/"                  append  /
350  ARCL L
351  "~="                 append =
352  ARCL Y
353  FIX 4
354  SF 29
355  PROMPT
356  END

( 513 bytes / SIZE 018 )
 

Example1:      75 - 100 - 25 - 3 - 9 - 6  //  758             Store these 7 numbers into R01 thru R07  respectively

   XEQ "LCEB"  >>>>     "75+3=78"       ( in 1 minute )
                           R/S        "78/6=13"
                           R/S        "100-13=87"
                           R/S        "87*9=783"
                           R/S        "783-25=758"

Example2:     4 - 7 - 50 - 1 - 4 - 100  //  903                4  STO 01  .........................  903  STO 07

   XEQ "LCEB"   >>>>   "100/4=25"        ( in 4 minutes )
                            R/S      "25-4=21"
                            R/S      "50-7=43"
                            R/S      43*21=903"

Example3:     3 - 7 - 7 - 50 - 1 - 8  //  947                   3  STO 01  ............................  947  STO 07

    XEQ "LCEB"   >>>>  the HP-41 displays  "Nb NOT FOUND"  about 6 minutes later

-However, there is a solution ( see below )
 

Remarks:

-Press  XEQ 10  to display again a solution in 1 operation
 -----   XEQ 09  ---------------------------- 2 ----------s
 -----   XEQ 08  ---------------------------- 3 -----------
 -----   XEQ 07 ----------------------------  4 -----------
 -----   XEQ 06 ----------------------------  5 -----------

-In order to decrease the execution time, flags F05 F06 F07 are used to avoid 2 successive additions and/or subtractions
  in the beginning of the search ( i-e at the end of the solutions ).
-Additions and subtractions are only computed after a division or a multiplication and a very simple result like  100 + 7 = 107 ,  107 + 25 = 132  cannot be found!
 ( delete lines 157 - 144 - 143 - 28 - 19  to allow this kind of solutions )
-Moreover, the multiplication doesn't appear in the beginning of the tree ( so, a solution never ends by a division )
 and many other solutions are skipped.

-Despite all these limitations, this program can solve about 90% of the soluble problems! ( only 80% if you delete lines 40 to 124 )
-Execution times are usually a few minutes ( less than 20 minutes apparently )

-Improvements are easy to make: delete all the lines involving flags F05 F06 F07 and a solution with 5 additions is now possible.
-Unfortunately, execution time can reach several hours... unless you are using an emulator like V41 in turbo mode,
 ( the several hours are reduced to less than 1 minute! )

-On the other hand, you can also add other operations:
  for instance, add  RCL 07  RCL 01  *  STO 08  XEQ 02  after line 23  and try example 3 again

-Your HP-41 now yields in 48 seconds:

                      "50+8=58"
          R/S      "58*7=406"
          R/S      "406*7=2842"
          R/S      "2842-1=2841"
          R/S      "2841/3=947"

-There are 2 minor defects:
   1-The solution in zero operation:  100 = 100  cannot be found, but a calculator is not absolutely necessary to find this result!
   2-The HP-41 displays "2+*2=4" instead of "2+2=4" or "2*2=4"
-Of course, this program can use other integers:
-For instance, with   32 - 41 - 55 - 48 - 49 - 67  //  2007

   XEQ "LCEB"  >>>>   "49-41=8"
                            R/S     "48/8=6"
                            R/S     "67-6=61"
                            R/S     "61*32=1952"
                            R/S     "1952+55=2007"
 
 

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