Sunday Times Teaser 2547 – Multiple Celebration

by R Nayler

Published: 17 July 2011 (link)

Today is my birthday and the birthday of my granddaughter Imogen. My age today is a whole-number multiple of hers, and this has been true on one third of our joint anniversaries.

If we both live until I am six times her current age, then my age will be a multiple of hers on two more birthdays.

How old are we today?

One Comment Leave one →

Brian Gladman permalink


from itertools import count

# for the age of the grand-daughter from 'frm' to 'to' inclusive,
# work out on how many anniversaries the grandfather's age will 
# be a multiple of that of the granddaughter
def count_multiples(gf_age, gd_age, frm, to):
  m = [1 for x in range(frm, to + 1) if (gf - gd + x) % x == 0]
  return len(m)

# consider the granddaughter's age
for gd in range(1, 31):
  
  # and the possible multiples for the grandfather's age
  for gf in range(gd, 6 * gd, gd):

    # up to now the grandfather's age has been a multiple of
    # the granddaughter's on a third of their joint birthdays
    if 3 * count_multiples(gf, gd, 1, gd) == gd:
      
      # in the future, until the grandfather is more than six 
      # times the granddaughter's current age,  one will be a 
      # multiple of the other on two occasions
      if count_multiples(gf, gd, gd + 1, 7 * gd - gf) == 2:
        print('Their ages are {} and {}.'.format(gd, gf))
        break
  else:
    continue
  break

from itertools import count

# for the age of the grand-daughter from 'frm' to 'to' inclusive,

# work out on how many anniversaries the grandfather's age will

# be a multiple of that of the granddaughter

def count_multiples(gf_age, gd_age, frm, to):

m = [1 for x in range(frm, to + 1) if (gf - gd + x) % x == 0]

return len(m)

# consider the granddaughter's age

for gd in range(1, 31):

# and the possible multiples for the grandfather's age

for gf in range(gd, 6 * gd, gd):

# up to now the grandfather's age has been a multiple of

# the granddaughter's on a third of their joint birthdays

if 3 * count_multiples(gf, gd, 1, gd) == gd:

# in the future, until the grandfather is more than six

# times the granddaughter's current age, one will be a

# multiple of the other on two occasions

if count_multiples(gf, gd, gd + 1, 7 * gd - gf) == 2:

print('Their ages are {} and {}.'.format(gd, gf))

break

else:

continue

break

Sunday Times Teaser 2547 – Multiple Celebration

by R Nayler

Published: 17 July 2011 (link)

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