Sunday Times Teaser 2888 – Two Sums

by Graham Smithers

Published January 28 2018 (link)

Digits have been systematically replaced by letters to give:

ONE + ONE = TWO

ONE + FOUR = FIVE

No number consists of a consecutive set of digits.

What number is represented by FIFTEEN?

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Brian Gladman permalink

Using my alphametic sum solver that is available here: alphasum.py


from alphasum import AlphaSum

# find solutions for the first sum
c1 = AlphaSum(['ONE', 'ONE'], 'TWO')
for s in c1.solve():
  # check that ONE and TWO don't have digits in a consecutive set
  s1, s2 = set(s[c] for c in 'ONE'), set(s[c] for c in 'TWO')
  if all(max(x) - min(x) != len(x) - 1 for x in (s1, s2)):
    # ind solutions for the second sum that are consistent with the first
    c2 = AlphaSum(['ONE', 'FOUR'], 'FIVE', l2d=s)
    for t in c2.solve():
      # check that FOUR and FIVE don't have digits in a consecutive set
      s3, s4 = set(t[c] for c in 'FOUR'), set(t[c] for c in 'FIVE')
      if all(max(x) - min(x) != len(x) - 1 for x in (s3, s4)):
        # output details of the two sums and FIFTEEN as a number
        print(c1.output())
        print(c2.output())
        print(f"\nFIFTEEN = {c2.substitute('FIFTEEN')}")

from alphasum import AlphaSum

# find solutions for the first sum

c1 = AlphaSum(['ONE', 'ONE'], 'TWO')

for s in c1.solve():

# check that ONE and TWO don't have digits in a consecutive set

s1, s2 = set(s[c] for c in 'ONE'), set(s[c] for c in 'TWO')

if all(max(x) - min(x) != len(x) - 1 for x in (s1, s2)):

# ind solutions for the second sum that are consistent with the first

c2 = AlphaSum(['ONE', 'FOUR'], 'FIVE', l2d=s)

for t in c2.solve():

# check that FOUR and FIVE don't have digits in a consecutive set

s3, s4 = set(t[c] for c in 'FOUR'), set(t[c] for c in 'FIVE')

if all(max(x) - min(x) != len(x) - 1 for x in (s3, s4)):

# output details of the two sums and FIFTEEN as a number

print(c1.output())

print(c2.output())

print(f"\nFIFTEEN = {c2.substitute('FIFTEEN')}")

Sunday Times Teaser 2888 – Two Sums

by Graham Smithers

Published January 28 2018 (link)

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