Friday the 13th Challenge, "Make 13 on the 13th"

[Egan Ford]

Using your favorite calculator find a future Friday the 13th where the sum of the digits that make up the date equals 13. E.g. if the date were MM/DD/YYYY (or DD.MM.YYYY) then M+M+D+D+Y+Y+Y+Y = 13. E.g. today is 13.03.2009, 1 + 3 + 3 + 2 + 9 <> 13.

Can you find the next one after that?

Hint: DD = 13 :-)

[Monte Dalrymple]

Using my trusty 41cv with time module:

5-13-2011
4-13-2012

are the next two

[hugh steers]

only 4 digit years!

07/13/10001

;-)

[Egan Ford]

Perhaps a future challenge, "Find the next 13 Friday the 13ths with digit sums of 13 with binary years, i.e. years with only 0s and 1s."

[hugh steers]

but more seriously,

does anyone have a better way to screen the digit sum.

i'm doing (y + m) == 0 mod 9, as a first approx, then summing the year and month digits for 9?

[Gerson W. Barbosa]

A straightforward approach on the HP 50g:

FR13:

<< { } RCLF -42 CF UNROT SWAP

130000 + 132009 SWAP

  FOR i i 1000000 / 1 12 

    FOR j 1 + DUP 0 TSTR 1 1 

SUB "F" ==

      IF

      THEN DUP 1000000 * SOD

13 ==

        IF 

        THEN DUP ROT + SWAP

        END

      END

    NEXT DROP

  NEXT REVLIST SWAP STOF

>>

SOD:

<< 0 SWAP 1 8

   START 10 / DUP FP 10 * ROT + 

SWAP IP

  NEXT DROP

>>

2040 FR13 returns {5.132011 4.132012 12.132013 2.132032}

Hopefully no typo (no connectivity kit installed on this computer).

Regards,

Gerson.

[Gerson W. Barbosa]

It's better to replace FOR j with START in the program above since the local variable j is never used.

Alternative SOD (sum of digits) routine:

SOD2:

<< DUP LN pi sqrt * SWAP 10 MOD + IP >>

It works for the following random examples:

7221961, 12345678, 41179453, 79, 9612 ;-)

It would be great if such a formula existed...

---------------------

Just a curiosity. These are all ocurrences of those Fridays the 13th in the period from 1583 to 9999:

{ 1.132006 10.132006 5.132011 4.132012 12.132013 2.132032 1.132051 10.132051 5.132101 2.132122 11.132122 1.132141 10.132141 1.132204 4.13221 12.132211 11.132212 4.1323 12.132301 2.13232 6.133 3.133012 1.133032 11.13304 2.133103 11.133103 1.133122 10.133122 1.133212 11.13322 1.133302 10.133302 4.134001 12.134002 3.13402 1.13404 2.134111 11.134111 1.13413 10.13413 2.134201 11.134201 10.13422 10.1344 3.135001 1.135111 10.135111 10.138 }

Edited: 15 Mar 2009, 7:14 p.m.

[Egan Ford]

Quote:

---

It would be great if such a formula existed...

---

http://mathworld.wolfram.com/DigitSum.html

Clearly there is a pattern, but nothing to simply return a digit sum.

[Nigel Bamber]

Thanks for the interesting and enjoyable challenge Egan, which I solved by writing my first proper 'program' for 25 years on my I41cx+ !

I am not sure it was the most elegant or efficient but it worked in the end , once I had worked out the differences in the effects of a XEQ and a GOTO jump.

Great fun.

Nigel

[Egan Ford]

You are very welcome.

[Nigel Bamber]

Thanks for the interesting and enjoyable challenge Egan, which I solved by writing my first proper 'program' for 25 years on my I41cx+ !

I am not sure it was the most elegant or efficient but it worked in the end , once I had worked out the differences in the effects of a XEQ and a GOTO jump.

Great fun.

Nigel

[Egan Ford]

Quote:

---

Using your favorite calculator find a future Friday the 13th where the sum of the digits that make up the date equals 13. E.g. if the date were MM/DD/YYYY (or DD.MM.YYYY) then M+M+D+D+Y+Y+Y+Y = 13. E.g. today is 13.03.2009, 1 + 3 + 3 + 2 + 9 <> 13.

Can you find the next one after that?

---

Thanks to all that participated and provided solutions.

As Monte quickly pointed out the first two are:

5-13-2011 and 4-13-2012

I created 3 solutions for the 12C. The 12C has two date functions:

1. DATE. Put a date in Y and a number in X and DATE will compute the future (or past) date and will also display the day-of-week, however the day-of-week is not stored, so it cannot be used in a program.
   
2. Delta Days. Put two dates on the stack and DDYS will return the difference in days.
   

My first program uses brute force to find the next and future Friday the 13ths with a digit sum of 13. To use, set the 12C in D.MY mode (cannot be programmed) and input any Friday date on the stack in D.MY format (e.g. 13.032009) and then press R/S. This program will test each Friday until another 13th is found, then a digit sum is used to check. After discovered you can press R/S again to get the next date.

NOTE: The DATE function includes a built-in PSE. Yup, its slow.

Time to first solution: 7 min 26 sec

Code:

01  f6          14  Rv          27  x=0         

02  ENTER       15  STO 1       28  GTO 30      

03  7           16  0           29  GTO 20      

04  DATE        17  STO 0       30  RCL 0       

05  ENTER       18  RCL 1       31  9           

06  INTG        19  FRAC        32  -           

07  1           20  1           33  x=0         

08  3           21  0           34  GTO 37      

09  -           22  x           35  RCL 1       

10  x=0         23  INTG        36  GTO 02      

11  GTO 14      24  STO+ 0      37  RCL 1       

12  Rv          25  LSTx        

13  GTO 02      26  FRAC        

My 2nd program works like the first, but skips by month. To use, set the 12C in M.DY mode and input in any 2009 or later 13th (e.g. 3.132009) and press R/S. After discovered you can press R/S again to get the next date.

Clearly skipping by month instead of week should be ~4x faster. However, this code is a bit more complicated because there is no easy way to check that each 13th of each month is on a Friday. The constant 12.282008 is a Sunday and is used to calculate day-of-week.

Time to first solution: 2 min 5 sec

Code:

01  STO 1           22  -               43  x               64  0               

02  f6              23  1               44  -               65  STO 0           

03  1               24  EEX             45  5               66  x<>y            

04  2               25  6               46  -               67  1               

05  .               26  CHS             47  x=0             68  0               

06  2               27  +               48  GTO 51          69  x               

07  8               28  GTO 33          49  RCL 1           70  INTG            

08  2               29  Rv              50  GTO 14          71  STO+ 0          

09  0               30  Rv              51  RCL 1           72  LSTx            

10  0               31  1               52  FRAC            73  FRAC            

11  8               32  +               53  LSTx            74  x=0             

12  STO 2           33  STO 1           54  INTG            75  GTO 77          

13  Rv              34  RCL 2           55  EEX             76  GTO 67          

14  ENTER           35  RCL 1           56  2               77  RCL 0           

15  INTG            36  DELTA DAYS      57  /               78  9               

16  1               37  ENTER           58  x<>y            79  -               

17  1               38  ENTER           59  .               80  x=0             

18  x<>y            39  7               60  1               81  GTO 84          

19  x<=y            40  /               61  3               82  RCL 1           

20  GTO 29          41  INTG            62  -               83  GTO 14          

21  Rv              42  7               63  +               84  RCL 1        

My final program takes a 4 digit year as the input and returns a "magic" number that represents all the months with Friday the 13ths. Unfortunately I ran out of steps (and time) and was unable to generalize this to produce exact solutions without a bit of aid.

Magic Number Table:

Magic Number     Months with Friday the 13ths

------------     ----------------------------

     1           May

     2           August

     2           February, August (leap year)

     3           February, March, November

     3           March, November (leap year)

     4           June

     5           September, December

     6           April, July

     7           January, October

     7           January, April, July (leap year)

E.g. 2011 will return 1, so 05-13-2011 is a Friday the 13th. Do the digit sum manually.

E.g. 2012 will return 6, so 04-13-2012 and 06-13-2012 are both Friday the 13ths. Again do the digit sum manually.

E.g. 2020 will return 3, but 2020 is a leap year, so only 03-13-2020 and 11-13-2020 are Friday the 13ths.

4046 is the largest year supported by the 12C.

Code:

01  STO 1           17  1               33  4               49  0               

02  1               18  .               34  /               50  0               

03  2               19  0               35  FRAC            51  /               

04  .               20  1               36  x=0             52  FRAC            

05  2               21  +               37  GTO 39          53  x=0             

06  8               22  DELTA DAYS      38  GTO 56          54  GTO 56          

07  2               23  ENTER           39  RCL 1           55  GTO 58          

08  0               24  ENTER           40  4               56  1               

09  0               25  7               41  0               57  STO- 2          

10  8               26  /               42  0               58  ENTER           

11  STO 0           27  INTG            43  /               59  5               

12  RCL 1           28  7               44  FRAC            60  RCL 2           

13  1               29  x               45  x=0             61  1               

14  EEX             30  -               46  GTO 58          62  -               

15  6               31  STO 2           47  RCL 1           63  -               

16  /               32  RCL 1           48  1               

Edited: 20 Mar 2009, 12:39 a.m.