Sunday Times Teaser 2602 – Over Fifty Years

by Andrew Skidmore

Published: 5 August 2012 (link)

We have now had over fifty years of Teasers and to celebrate this I found three special numbers using only non-zero digits and I wrote the numbers down in increasing order. Then I consistently replaced all the digits by letters, with different letters for different digits.

In this way the numbers became FIFTY YEARS TEASER. In fact the third number was the sum of the other two.

Which number does TEASER represent?

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briangladman permalink

Here is a solution:


from itertools import permutations

# T is 1 by inspection 
m = {'T':'1'}
words = ('FIFTY', 'YEARS', 'TEASER')
# find the letters other than T
w = set(''.join(words)) - set(('T',))
# now permute digits other than 0 and 1
for p in permutations('23456789'):
  # set dictionary mp from letters to digits
  m.update(zip(w, p))
  # now find the numeric values of the three words
  x, y, z = tuple(int(''.join(m[x] for x in w)) for w in words)
  # and acheck the constraints
  if x < y and z == x + y:
    print('{:d} ({:d}, {:d})'.format(z, x, y))

from itertools import permutations

# T is 1 by inspection

m = {'T':'1'}

words = ('FIFTY', 'YEARS', 'TEASER')

# find the letters other than T

w = set(''.join(words)) - set(('T',))

# now permute digits other than 0 and 1

for p in permutations('23456789'):

# set dictionary mp from letters to digits

m.update(zip(w, p))

# now find the numeric values of the three words

x, y, z = tuple(int(''.join(m[x] for x in w)) for w in words)

# and acheck the constraints

if x < y and z == x + y:

print('{:d} ({:d}, {:d})'.format(z, x, y))

Sunday Times Teaser 2602 – Over Fifty Years

by Andrew Skidmore

Published: 5 August 2012 (link)

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