Sunday Times Teaser 2832 – A New Year Reminiscence

by Victor Bryant

Published: 1 January 2017 (link)

Whilst filing away last year’s diary this morning I came across an old diary from my teenage years. In it I can see that in one particular month I went to four parties, three of them being on Saturdays and the other on a Sunday. I wrote down the four dates of the parties in words (in the format “January first” etc) and found that each of the dates used a different prime number of letters.

What were the four dates that I wrote down?

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Brian Gladman permalink


from collections import defaultdict
from itertools import combinations, product

months = ( 'January', 'February', 'March', 'April', 'May', 
           'June', 'July', 'August', 'September', 'October', 
           'November', 'December' )

days = ( 'first', 'second', 'third', 'fourth', 'fifth', 'sixth', 
         'seventh', 'eighth', 'ninth', 'tenth', 'eleventh', 'twelfth', 
         'thirteenth', 'fouteenth', 'fifteenth', 'sixteenth', 
         'seventeenth', 'eighteenth','nineteenth', 'twentieth', 
         'twentyfirst', 'twentysecond', 'twentythird','twentyfourth',
         'twentyfifth', 'twentysixth', 'twentyseventh', 'twentyeighth', 
         'twentyninth', 'thirtieth', 'thirtyfirst' )

# days in month
dim = ( 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 )
        
primes = { 2, 3, 5, 7, 11, 13, 17, 19 }

# map the months to the number of letters in (month, day) dates
# that are prime and then to the days in the month with dates
# that have this number of letters
m2l2d = defaultdict(lambda:defaultdict(list))
for i, m in enumerate(months):
  for j, d in enumerate(days[:dim[i]]):
    l = len(m + d)
    if l in primes:
      m2l2d[m][l].append(j + 1)

# consider each month
for m in m2l2d.keys():
  # consider all combinations of four different date lengths
  for l4 in combinations(m2l2d[m], 4):
    # and all combinations of days with these lengths
    for d4 in product(*(m2l2d[m][l] for l in l4)):
      # look for a set of four days with three on the same
      # weekday and one on the following weekday
      wk = [d % 7 for d in d4]
      ct = {wk.count(x):x for x in wk}
      try:
        if (ct[1] - ct[3]) % 7 == 1:
          print('{} {}th, {}th, {}th and {}th.'.format(m, *d4))
      except KeyError:
        continue

from collections import defaultdict

from itertools import combinations, product

months = ( 'January', 'February', 'March', 'April', 'May',

'June', 'July', 'August', 'September', 'October',

'November', 'December' )

days = ( 'first', 'second', 'third', 'fourth', 'fifth', 'sixth',

'seventh', 'eighth', 'ninth', 'tenth', 'eleventh', 'twelfth',

'thirteenth', 'fouteenth', 'fifteenth', 'sixteenth',

'seventeenth', 'eighteenth','nineteenth', 'twentieth',

'twentyfirst', 'twentysecond', 'twentythird','twentyfourth',

'twentyfifth', 'twentysixth', 'twentyseventh', 'twentyeighth',

'twentyninth', 'thirtieth', 'thirtyfirst' )

# days in month

dim = ( 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 )

primes = { 2, 3, 5, 7, 11, 13, 17, 19 }

# map the months to the number of letters in (month, day) dates

# that are prime and then to the days in the month with dates

# that have this number of letters

m2l2d = defaultdict(lambda:defaultdict(list))

for i, m in enumerate(months):

for j, d in enumerate(days[:dim[i]]):

l = len(m + d)

if l in primes:

m2l2d[m][l].append(j + 1)

# consider each month

for m in m2l2d.keys():

# consider all combinations of four different date lengths

for l4 in combinations(m2l2d[m], 4):

# and all combinations of days with these lengths

for d4 in product(*(m2l2d[m][l] for l in l4)):

# look for a set of four days with three on the same

# weekday and one on the following weekday

wk = [d % 7 for d in d4]

ct = {wk.count(x):x for x in wk}

try:

if (ct[1] - ct[3]) % 7 == 1:

print('{} {}th, {}th, {}th and {}th.'.format(m, *d4))

except KeyError:

continue

Sunday Times Teaser 2832 – A New Year Reminiscence

by Victor Bryant

Published: 1 January 2017 (link)

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