Sunday Times Teaser 2577 – Number Waves

by Graham Smithers

Published: 12 February 2012 (link)

I challenged Sam to find a 9-figure number using all of the digits 1 to 9 such that each digit occupying an even position was equal to the sum of its adjacent digits. (For example, the digit occupying position four would be equal to the sum of the digits occupying positions three and five.) Sam produced a solution that was exactly divisible by its first digit, by its last digit, and by 11. What was his number?

2 Comments Leave one →

Brian Gladman permalink


from functools import reduce

def solve(seq=[]):
  ln = len(seq)
  # do we have nine digits?
  if ln == 9:
    yield seq
  # are we adding a digit in an odd position
  # (counting from the units digit as odd)
  elif ln and not ln % 2:
    # we need a value that makes its sum with the last
    # but one digit equal to the previous digit
    v = seq[-1] - seq[-2]
    # check it is a valid digit and not already present
    if 0 <= v < 10 and v not in seq:
      yield from solve(seq + [v])
  else:
    # otherwise add any unused digit (except 0 as a 
    # leading digit)
    s = set(range(0 if len(seq) else 1, 10))
    for d in s.difference(seq):
      yield from solve(seq + [d])

for s in solve():
  # form the number
  nbr = reduce(lambda x, y: 10 * x + y, s)
  # the last digit cannot be zero
  if s[-1]:
    if not (nbr % s[0] or nbr % s[-1] or nbr % 11):
      print('His number was {}.'.format(nbr))

from functools import reduce

def solve(seq=[]):

ln = len(seq)

# do we have nine digits?

if ln == 9:

yield seq

# are we adding a digit in an odd position

# (counting from the units digit as odd)

elif ln and not ln % 2:

# we need a value that makes its sum with the last

# but one digit equal to the previous digit

v = seq[-1] - seq[-2]

# check it is a valid digit and not already present

if 0 <= v < 10 and v not in seq:

yield from solve(seq + [v])

else:

# otherwise add any unused digit (except 0 as a

# leading digit)

s = set(range(0 if len(seq) else 1, 10))

for d in s.difference(seq):

yield from solve(seq + [d])

for s in solve():

# form the number

nbr = reduce(lambda x, y: 10 * x + y, s)

# the last digit cannot be zero

if s[-1]:

if not (nbr % s[0] or nbr % s[-1] or nbr % 11):

print('His number was {}.'.format(nbr))

geoffrounce permalink


from itertools import permutations

for p in permutations('123456789',9):
    a,b,c,d,e,f,g,h,i = p
    num = int(a+b+c+d+e+f+g+h+i)
    if int(b) == int(a) + int(c) and int(d) == int(c) + int(e) 
       and int(f) == int(e) + int(g) and int(h) == int(g) + int(i):
        if num % int(a) == 0 and num % int(i) == 0 and num % 11 == 0:
            print('Number = ', num)

from itertools import permutations

for p in permutations('123456789',9):

a,b,c,d,e,f,g,h,i = p

num = int(a+b+c+d+e+f+g+h+i)

if int(b) == int(a) + int(c) and int(d) == int(c) + int(e)

and int(f) == int(e) + int(g) and int(h) == int(g) + int(i):

if num % int(a) == 0 and num % int(i) == 0 and num % 11 == 0:

print('Number = ', num)

Sunday Times Teaser 2577 – Number Waves

by Graham Smithers

Published: 12 February 2012 (link)

Leave a Reply Cancel reply

Recent Posts

Recent Comments

Archives

Categories

Meta