Sunday Times Teaser 2701 – Flipping Ages!

by Robin Nayler

The ages of ten people in my family form an arithmetic progression. My age has the same digits as that of my wife but in reverse order. This is also true for my mother and my sister, my daughter and her daughter, and my son and his son. Also the product of my brother’s age and that of his son is equal to the year of birth of one of the ten people.

What are the ages of my brother, my sister and myself (in that order)?

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from operator import itemgetter

# for formatting the output
fs = 'My brother is {}, my sister is {}, and I am {}.'

# the current year
now = 2014

# for two digit numbers to be the reverse of each other
# their difference must be a multiple of nine,  which
# is hence the increment in the arithmetic progression
for a in range(1, 37):
  # we need ten numbers for the ages
  ages = tuple(a + 9 * i for i in range(10))
  
  # find four reversible pairs and the leftovers 
  # (i.e. the ages of the brother and his son) 
  pairs, leftovers = [], []
  for n in ages:
    r = 10 * n if n < 10 else int(str(n)[::-1])
    if r != n and r in ages:
      if n < r:
        pairs.append((n, r))
    else:
      leftovers.append(n)
      
  if len(pairs) == 4 and len(leftovers) == 2:
    # sort the pairs in order of their oldest members
    pairs = tuple(sorted(pairs, key=itemgetter(1)))
    (son, brother) = leftovers
    # the product of the brother's and his son's age
    # must give a sensible year of birth with an age
    # now that matches one of our ages
    age = now - son * brother
    if age in ages or age - 1 in ages:
      
      # considering the older members of each pair, the
      # son and the daughter are the lowest, myself or
      # my wife are next and my mother is last - check
      # that the son's and daughter's ages are not too
      # far apart
      if pairs[1][1] - pairs[0][1] < 50:
        # the sister is paired with the mother and my
        # wife and I are the third pair
        sister, mum = pairs[3]
        us = pairs[2]
        # ensure my age relative to my mum is sensible
        me, = tuple(x for x in us if 12 < mum - x < 50)
        print(fs.format(brother, sister, me))

from operator import itemgetter

# for formatting the output

fs = 'My brother is {}, my sister is {}, and I am {}.'

# the current year

now = 2014

# for two digit numbers to be the reverse of each other

# their difference must be a multiple of nine, which

# is hence the increment in the arithmetic progression

for a in range(1, 37):

# we need ten numbers for the ages

ages = tuple(a + 9 * i for i in range(10))

# find four reversible pairs and the leftovers

# (i.e. the ages of the brother and his son)

pairs, leftovers = [], []

for n in ages:

r = 10 * n if n < 10 else int(str(n)[::-1])

if r != n and r in ages:

if n < r:

pairs.append((n, r))

else:

leftovers.append(n)

if len(pairs) == 4 and len(leftovers) == 2:

# sort the pairs in order of their oldest members

pairs = tuple(sorted(pairs, key=itemgetter(1)))

(son, brother) = leftovers

# the product of the brother's and his son's age

# must give a sensible year of birth with an age

# now that matches one of our ages

age = now - son * brother

if age in ages or age - 1 in ages:

# considering the older members of each pair, the

# son and the daughter are the lowest, myself or

# my wife are next and my mother is last - check

# that the son's and daughter's ages are not too

# far apart

if pairs[1][1] - pairs[0][1] < 50:

# the sister is paired with the mother and my

# wife and I are the third pair

sister, mum = pairs[3]

us = pairs[2]

# ensure my age relative to my mum is sensible

me, = tuple(x for x in us if 12 < mum - x < 50)

print(fs.format(brother, sister, me))

Sunday Times Teaser 2701 – Flipping Ages!

by Robin Nayler

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