Sunday Times Teaser 2535 – Eastertide

by Andrew Skidmore

Published: 24 April 2011 (link)

In the following division sum I have consistently replaced digits with letters, with different letters used for different digits. All three numbers featured are even:

EASTER ÷ TIDE = EGG

What is the numerical value of my TEASER?

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from itertools import permutations
from functools import reduce

# permute even digits for known 'even' letters 
for E, G, R in permutations(range(0, 10, 2), 3):
  
  # now permute the remaining digits for I, D and T 
  for I, D, T in permutations(set(range(10)).difference([E, G, R]), 3):

    # the three values  
    tide = 1000 * T + 100 * I + 10 * D + E
    egg = 100 * E + 11 * G
    easter = tide * egg

  # check that EASTER is the right length    
    if 100000 <= easter < 1000000:
      
      # now check that known letter values in EASTER are correct
      e1, A, S, t1, e2, r1 = map(int, str(tide * egg))
      if e1 == e2 == E and t1 == T and r1 == R:
        
        teaser = reduce(lambda x, y: 10 * x + y, (T, E, A, S, E, R))
        print('TEASER = {}'.format(teaser))

from itertools import permutations

from functools import reduce

# permute even digits for known 'even' letters

for E, G, R in permutations(range(0, 10, 2), 3):

# now permute the remaining digits for I, D and T

for I, D, T in permutations(set(range(10)).difference([E, G, R]), 3):

# the three values

tide = 1000 * T + 100 * I + 10 * D + E

egg = 100 * E + 11 * G

easter = tide * egg

# check that EASTER is the right length

if 100000 <= easter < 1000000:

# now check that known letter values in EASTER are correct

e1, A, S, t1, e2, r1 = map(int, str(tide * egg))

if e1 == e2 == E and t1 == T and r1 == R:

teaser = reduce(lambda x, y: 10 * x + y, (T, E, A, S, E, R))

print('TEASER = {}'.format(teaser))

Sunday Times Teaser 2535 – Eastertide

by Andrew Skidmore

Published: 24 April 2011 (link)

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