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



#13

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 :-)


#14

Using my trusty 41cv with time module:

5-13-2011
4-13-2012

are the next two


#15

only 4 digit years!

07/13/10001

;-)


#16

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."

#17

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?

#18

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.


#19

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.


#20

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.

#21

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


#22

You are very welcome.

#23

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

#24

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.


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