Here's my code for Ting's 4/24 programmer's challenge.

I've included the Forth version, as well as a Python version which I used to convince myself I had a plausible solution.

The Python version is of course longer, slower, and uses floating point.


-Brad Nelson
bnels123@gmail.com

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365256363 constant year
 29530689 constant month
  1000000 constant day

: >date ( m d y -- dd ) year * swap 1- day * + swap 1- month * + ;
: date> ( dd -- m d y ) year /mod >r month /mod 1+ swap day / 1+ r> ;
: date. ( dd -- ) date> >r >r
                  s>d <# # # #> type ." /"
                  r> s>d <# # # #> type ." /"
                  r> s>d <# # # # # #> type ;

: skew ( n period -- n ) mod day / ;
: aligns? ( a b period -- f ) dup >r skew swap r> skew = ;

: spring-equinox?   3 21 2010 >date year aligns? ;
: full-moon?   3 29 2010 >date month aligns? ;
: thursday?   3 25 2010 >date 7 day * aligns? ;

: yesterday ( dd -- dd ) day - ;

: ??true ( T -- 1 break ) if drop 1 rdrop then ;
: ??false ( F -- 0 break ) if drop 0 rdrop then ;
: passover? ( dd -- f) dup full-moon? 0= ??false
                       begin yesterday
                         dup spring-equinox? ??true
                         dup full-moon? ??false
                       again ;

: target? ( dd -- f) yesterday dup passover? swap thursday? and ;

: check ( dd -- ) dup target? if date. cr else drop then ;
: solve   20000 1000 do i day * check loop ;

solve
bye


-------

#!/usr/bin/python

YEAR = 365.256363
MONTH = 29.530689


def DateToDay(month, day, year):
  return year * YEAR + (month - 1) * MONTH + (day - 1)

def DayToDate(day):
  year = int(day / YEAR)
  day -= year * YEAR
  month = int(day/ MONTH)
  day -= month * MONTH
  return ((month + 1), int(day + 1), year)

def Aligns(a, b, interval):
  return int(a % interval) == int(b % interval)

def IsSpringEquinox(day):
  return Aligns(DateToDay(3, 21, 2010), day, YEAR)

def IsFullMoon(day):
  return Aligns(DateToDay(3, 29, 2010), day, MONTH)

def IsThursday(day):
  return Aligns(DateToDay(3, 25, 2010), day, 7)

def DayToWeekday(day):
  wd = int(day % 7)
  return ('Sun', 'Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat')[wd]

def IsPassover(day):
  if not IsFullMoon(day): return False
  while True:
    day -= 1
    if IsSpringEquinox(day): return True
    if IsFullMoon(day): return False

def IsTarget(day):
  return IsPassover(day - 1) and IsThursday(day - 1)

for x in range(1000, 20000):
  if IsTarget(x):
    print '%02d/%02d/%04d' % DayToDate(x), DayToWeekday(x)