Killer Counting Problem from Ashish

[bplus]

Ashish:

Do you really want to play with numbers.... I have a puzzle for you then
Create a 10 digit number so that the first digit is the number of zeros in the number, the second digit is the number of ones in the number, the third digit is the number of twos, etc.

Here is my count(s):

Code: QB64: [Select]

1. _TITLE "Killer Counting Problem from Ashish" 'b+ 2020-06-03
2. DIM d(9)
3. s$ = STRING$(3, "5") + STRING$(7, "0") '<<< doesn't matter where you start even a string too long or short,  keep counts of digits under 10 though
4. PRINT s$
5. restart:
6. ERASE d
7. FOR i = 1 TO LEN(s$)
8.     m = VAL(MID$(s$, i, 1))
9.     d(m) = d(m) + 1
10. NEXT
11. n$ = ""
12. FOR i = 0 TO 9
13.     n$ = n$ + _TRIM$(STR$(d(i)))
14. NEXT
15. PRINT n$
16. s$ = n$
17. INPUT "OK press enter to continue, any else to quit "; continue$
18. IF LEN(continue$) = 0 THEN GOTO restart
19.  
20.  

[Ashish]

Is this program giving the possible solution? If yes, I do not find the correct one in your program.
BTW, qbkiller have already told me the answer at discord. He did that by writing a script in JavaScript.

One side note, This problem is not created by me or its made by me. The original problem is here - http://paulbourke.net/fun/zeros.html

Also, I was trying to solve this problem without using any computer program , etc but since qbkiller had told me the answer, I have lost
all the interest in this very good puzzle.

[STxAxTIC]

By hand I started with

0000000000

So maybe

9000000000

but then

8100000000

but finally

6210001000

worked.

[bplus]

Is this program giving the possible solution? If yes, I do not find the correct one in your program.
BTW, qbkiller have already told me the answer at discord. He did that by writing a script in JavaScript.

One side note, This problem is not created by me or its made by me. The original problem is here - http://paulbourke.net/fun/zeros.html

Also, I was trying to solve this problem without using any computer program , etc but since qbkiller had told me the answer, I have lost
all the interest in this very good puzzle.

Oh looks like STxAxTIC has a solution but is it the only one? LOL

@Ashish Not posted as solution, I didn't think there might be one. I thought if there were one then the code would get to it, sort of like a limit, but alas it didn't. Looks like it was close. I was impressed that any string of digits kept going to that sequence of two numbers after say 5 iterations.

BTW, qbkiller have already told me the answer at discord. He did that by writing a script in JavaScript.

@qbkiller101  I'd love to see it! :)

[Ashish]

Oh looks like STxAxTIC has a solution but is it the only one? LOL

Yeah, He has the solution, but I *do not* know whether there is multiple solutions or not.

[SMcNeill]

Just curious, but isn't the value reversed??

123....   

First digit would be 3, Second digit 2, Third digit 1...

With numbers, don't we count digits from right to left usually?  Ones, tens, hundreds, thousands...

(Not that it's a big deal, as you just reverse the solution, but as it sits, I *never* would've got it right.  My 6210001000 would end up being 0001000126, just because I think right to left in numerical digits.)

[qbkiller101]

Oh looks like STxAxTIC has a solution but is it the only one? LOL

@Ashish Not posted as solution, I didn't think there might be one. I thought if there were one then the code would get to it, sort of like a limit, but alas it didn't. Looks like it was close. I was impressed that any string of digits kept going to that sequence of two numbers after say 5 iterations.
@qbkiller101  I'd love to see it! :)

@bplus  same that static told :)

[bplus]

@bplus  same that static told :)

@qbkiller101 Yeah I assumed you got the answer but if you used a program that is different than just figuring from your head. It's the program I'd like to see. Is Java Script the first Programming Language you learned?

The digits do have to add up to 10, plug in permutations that add to 10 and using lowest digits?

I see Steve has found a 2nd solution, sorta :)

[SMcNeill]

@qbkiller101 Yeah I assumed you got the answer but if you used a program that is different that just figuring from your head. It's the program I'd like to see. Is Java Script the first Programming Language you learned?

The digits do have to add up to 10, plug in permutations that add to 10 and using lowest digits?

I see Steve has found a 2nd solution, sorta :)

Little Endian answer vs Big Endian.  It's the same value, just represented in reverse order.  ;)

[bplus]

Little Endian answer vs Big Endian.  It's the same value, just represented in reverse order.  ;)

Yeah, the people in Cleveland are missing the Endians this summer.

[bplus]

This code solves the problem 100 times in around 1/4 of a million Random Generated Solutions:

Code: QB64: [Select]

1. _TITLE "Killer Counting Problem Rnd Solver" 'b+ 2020-06-03
2. RANDOMIZE TIMER
3. DIM d(9)
4.  
5. restart:
6. iteration = iteration + 1
7. ERASE d
8. s$ = makeRnd10$
9. 's$ = "6210001000" 'check and make sure it recognizes a solve
10. FOR i = 1 TO LEN(s$)
11.     m = VAL(MID$(s$, i, 1))
12.     d(m) = d(m) + 1
13. NEXT
14. n$ = ""
15. FOR i = 0 TO 9
16.     n$ = n$ + _TRIM$(STR$(d(i)))
17. NEXT
18.  
19. PRINT _TRIM$(STR$(iteration)); "# "; "Rnd Sol'n: "; s$; " check: "; n$
20. IF s$ = n$ THEN
21.     solved = solved + 1
22.     PRINT _TRIM$(STR$(iteration)); "# "; "solved! "; _TRIM$(STR$(solved)); " times now."
23.     IF s$ <> "6210001000" THEN PRINT "Holy Mother of God a 2nd solution!!!!!": END
24.     IF solved = 100 THEN END 'ELSE _DELAY 2
25. END IF
26. 'INPUT "OK press enter to continue, any else to quit "; continue$
27. IF LEN(continue$) = 0 THEN GOTO restart
28.  
29. FUNCTION makeRnd10$ ()
30.     'generate a random solution keeping in mind:
31.     ' 1. the digits have to add to 10
32.     ' 2. the lower digits are way more likely than the higher digits 0's being most likely 9's least
33.     DIM d(9)
34.     FOR i = 0 TO 9
35.         r = INT(RND * (11 - l))
36.         WHILE r = 10
37.             r = INT(RND * (11 - l))
38.         WEND
39.         l = l + r
40.         'PRINT l;
41.         d(i) = r
42.     NEXT
43.     PRINT
44.     FOR i = 0 TO 9
45.         rs$ = rs$ + _TRIM$(STR$(d(i)))
46.     NEXT
47.     makeRnd10$ = rs$
48. END FUNCTION
49.  
50.  

[bplus]

You know, Steve might have a point if you look for the lowest numbered solution.

In fact, what if we just counted up and tested if it met the conditions of a solution?

[bplus]

Yeah, this proves there is only 1 soln and after an hour+ run. I edited code to bug out when found at 1000126.

Code: QB64: [Select]

1. _TITLE "Killer Counting Problem, Solve by Counting Up" 'b+ 2020-06-03
2. DIM solved$(10)
3. RANDOMIZE TIMER
4. DIM d(9)
5. DIM n AS _INTEGER64
6. FOR n = 1 TO 1000000000 '9 0's and 1 1?
7.     ' n = 1000126   'check soln stops
8.     ERASE d: tot = 0
9.     ns$ = RIGHT$(STRING$(10, "0") + _TRIM$(STR$(n)), 10)
10.     IF n MOD 1000000 = 1 THEN PRINT n, ns$, "solns:"; soln
11.  
12.     FOR i = 1 TO LEN(ns$)
13.         m = VAL(MID$(ns$, i, 1))
14.         d(m) = d(m) + 1
15.         tot = tot + m
16.     NEXT
17.     IF tot = 10 THEN
18.         ck$ = ""
19.         FOR i = 9 TO 0 STEP -1
20.             ck$ = ck$ + _TRIM$(STR$(d(i)))
21.         NEXT
22.         IF ck$ = ns$ THEN
23.             soln = soln + 1: solved$(soln) = ns$
24.             EXIT FOR 'only 1 soln so bug out
25.         END IF
26.     END IF
27.     'INPUT "OK "; cont$
28. NEXT
29. PRINT "All done!, # solutions found: "; soln 'OK there is only 1 soln so quit when have it
30. FOR i = 1 TO soln
31.     PRINT solved$(i)
32. NEXT
33.