Sunday Times Teaser 2792 – Easter Teaser

by Alan Bergson

Published: 27 March 2016 (link)

I have written down three numbers and then consistently replaced digits by letters, with different letters for different digits, to give:

EASTER SUNDAY TEASER.

In fact the first number is the lowest and one of these numbers is the sum of the other two.

What is this SUNDAY’s number?

2 Comments Leave one →

Brian Gladman permalink


from itertools import permutations
from functools import reduce

digits = set(range(10))
# permute diigits for A, E, R, S and T
for p in permutations(digits, 5):
  # map these letters to digits
  d = dict(zip('AERST', p))
  # form EASTER and TEASER and check that EASTER is less than TEASER
  easter = reduce(lambda x, y: 10 * x + y, (d[x] for x in 'EASTER'))
  teaser = reduce(lambda x, y: 10 * x + y, (d[x] for x in 'TEASER'))
  if easter < teaser:
    # form possible SUNDAY values, checking that the value is greater than EASTER
    for sunday in (teaser + easter, teaser - easter):
      if easter < sunday:
        # the digits in SUNDAY
        ss = set(int(x) for x in str(sunday))
        # extract the digits for S and A
        t = sunday // 100000, (sunday // 10) % 10
        # check that SUNDAY has six different digits including S and A and
        # that there are nine digits overall
        if len(ss) == 6 and t == (d['S'], d['A']) and len(set(p) | ss) == 9:
          fs = 'SUNDAY = {} (EASTER = {}, TEASER = {}).'
          print(fs.format(sunday, easter, teaser))

from itertools import permutations

from functools import reduce

digits = set(range(10))

# permute diigits for A, E, R, S and T

for p in permutations(digits, 5):

# map these letters to digits

d = dict(zip('AERST', p))

# form EASTER and TEASER and check that EASTER is less than TEASER

easter = reduce(lambda x, y: 10 * x + y, (d[x] for x in 'EASTER'))

teaser = reduce(lambda x, y: 10 * x + y, (d[x] for x in 'TEASER'))

if easter < teaser:

# form possible SUNDAY values, checking that the value is greater than EASTER

for sunday in (teaser + easter, teaser - easter):

if easter < sunday:

# the digits in SUNDAY

ss = set(int(x) for x in str(sunday))

# extract the digits for S and A

t = sunday // 100000, (sunday // 10) % 10

# check that SUNDAY has six different digits including S and A and

# that there are nine digits overall

if len(ss) == 6 and t == (d['S'], d['A']) and len(set(p) | ss) == 9:

fs = 'SUNDAY = {} (EASTER = {}, TEASER = {}).'

print(fs.format(sunday, easter, teaser))

Jim Randell permalink

I used the SubstitutedSum() solver from my enigma.py library:


from enigma import SubstitutedSum, printf

# try: EASTER + SUNDAY = TEASER and EASTER + TEASER = SUNDAY
for s in (['EASTER', 'SUNDAY', 'TEASER'], ['EASTER', 'TEASER', 'SUNDAY']):
  p = SubstitutedSum(s[:2], s[2])
  for r in p.solve():
    # check EASTER is the smaller term
    if r[s[0][0]] < r[s[1][0]]:
      SUNDAY = p.substitute(r, 'SUNDAY')
      p.solution(r)
      printf("SUNDAY={SUNDAY}")

from enigma import SubstitutedSum, printf

# try: EASTER + SUNDAY = TEASER and EASTER + TEASER = SUNDAY

for s in (['EASTER', 'SUNDAY', 'TEASER'], ['EASTER', 'TEASER', 'SUNDAY']):

p = SubstitutedSum(s[:2], s[2])

for r in p.solve():

# check EASTER is the smaller term

if r[s[0][0]] < r[s[1][0]]:

SUNDAY = p.substitute(r, 'SUNDAY')

p.solution(r)

printf("SUNDAY={SUNDAY}")

Although we can also run the cryptarithms from the command line directly using the enigma.py library:


% python enigma.py SubstitutedSum EASTER SUNDAY TEASER
[solving EASTER + SUNDAY = TEASER ...]
% python enigma.py SubstitutedSum EASTER TEASER SUNDAY
[solving EASTER + TEASER = SUNDAY ...]
A=7 D=2 E=3 N=6 R=5 S=8 T=4 U=1 Y=0 / 378435 + 437835 = 816270

% python enigma.py SubstitutedSum EASTER SUNDAY TEASER

[solving EASTER + SUNDAY = TEASER ...]

% python enigma.py SubstitutedSum EASTER TEASER SUNDAY

[solving EASTER + TEASER = SUNDAY ...]

A=7 D=2 E=3 N=6 R=5 S=8 T=4 U=1 Y=0 / 378435 + 437835 = 816270

Which shows us that there is only one possible solution anyway, without the need to do any further programming.

Sunday Times Teaser 2792 – Easter Teaser

by Alan Bergson

Published: 27 March 2016 (link)

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