Sunday Times Teaser 2738 – Prime Day for the Irish

by H Bradley and C Higgins

Published: 15 March 2015 (link)

St Patrick’s Day is March 17 and it is a prime day in many ways: What number month? 3; What number day? 17; How many letters in “March”? 5; How many days in March? 31.

I asked Pat the same questions about his birthday this year — but I simply asked whether the four answers were prime or not. When he had told me he said “now, if I told you its day of the week this year, you should be able to work out my birthday.” Then, without me actually being told the day, I was indeed able to work out his birthday.

What is his birthday?

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Brian Gladman permalink


from datetime import date
from calendar import month_name, monthrange
from collections import defaultdict

from number_theory import Primes

# dates are in this year
year = 2015

# store possible birthday dates indexed first on the
# four truth values and then on the day of the week
d1 = defaultdict(lambda: defaultdict(list))
for month in range(1, 13):
  # compile the three truth properties for the month
  month_length = monthrange(year, month)[1]
  t3 = tuple(x in Primes() for x in 
             (month, len(month_name[month]), month_length))
  
  for day in range(1, month_length + 1):
    # find the day of the week
    dow = date(year, month, day).weekday()
    # add the truth value for the day of the month and store results
    d1[t3 + (day in Primes(),)][dow].append((day, month))

d2 = defaultdict(list)
# now consider each of the sixteen combinations of truth properties 
for t4, d_dm in d1.items():
  # and look for days of the week that lead to a unique date
  for dow, l_bd in d_dm.items():
    if len(l_bd) == 1:
      d2[t4].append(l_bd[0])

# now look for a set of truth properties with only one unique date
for t4, l_bd in d2.items():
  if len(l_bd) == 1:
      print('His birthday is {} {}.'
            .format( l_bd[0][0], month_name[l_bd[0][1]]))

from datetime import date

from calendar import month_name, monthrange

from collections import defaultdict

from number_theory import Primes

# dates are in this year

year = 2015

# store possible birthday dates indexed first on the

# four truth values and then on the day of the week

d1 = defaultdict(lambda: defaultdict(list))

for month in range(1, 13):

# compile the three truth properties for the month

month_length = monthrange(year, month)[1]

t3 = tuple(x in Primes() for x in

(month, len(month_name[month]), month_length))

for day in range(1, month_length + 1):

# find the day of the week

dow = date(year, month, day).weekday()

# add the truth value for the day of the month and store results

d1[t3 + (day in Primes(),)][dow].append((day, month))

d2 = defaultdict(list)

# now consider each of the sixteen combinations of truth properties

for t4, d_dm in d1.items():

# and look for days of the week that lead to a unique date

for dow, l_bd in d_dm.items():

if len(l_bd) == 1:

d2[t4].append(l_bd[0])

# now look for a set of truth properties with only one unique date

for t4, l_bd in d2.items():

if len(l_bd) == 1:

print('His birthday is {} {}.'

.format( l_bd[0][0], month_name[l_bd[0][1]]))

Sunday Times Teaser 2738 – Prime Day for the Irish

by H Bradley and C Higgins

Published: 15 March 2015 (link)

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