Sunday Times Teaser 2605 – Simple Sums

by Graham Smithers

Published: 26 August 2012 (link)

I have taken some numbers and consistently replaced the digits by letters, with different letters for different digits. In this way:

TWO + TWO = FOUR
FIVE is prime
FIVE — TWO is prime
THREE is divisible by 3

Quelle est la valeur de HUIT?

2 Comments Leave one →

briangladman permalink

Another boring Alphametic 🙁 Here is my solution:


from itertools import permutations

# return a list of primes up to but not including n
def prime_list(n) :
  sieve = [False, False] + [True] * (n - 1)
  for i in range(2, int(n ** 0.5) + 1):
    if sieve[i] :
      m = n // i - i
      sieve[i * i : n + 1 : i] = [False] * (m + 1)
  return [ i for i in range(n + 1) if sieve[i] ]

pr = prime_list(2000)

# TWO + TWO = FOUR makes F = 1 and E is 3, 7 or 9
# because it is last digit of a four digit prime
for e in ('3', '7', '9'):
  # permute the remaining digits and put them in the map
  for p in permutations(set('023456789') - set((e,))):
    d = dict(zip('THIORUVWEF', p + ((e, '1'))))

    # check that T and H are not zero
    if '0' not in p[:2]:
      # check that FIVE is prime
      five = int(''.join(d[x] for x in 'FIVE'))
      if five in pr:
        # check FIVE - TWO is prime and TWO + TWO = FOUR
        two = int(''.join(d[x] for x in 'TWO'))
        four = int(''.join(d[x] for x in 'FOUR'))
        if five - two in pr and two + two == four:
          # check that THREE is a multiple of 3
          if int(''.join(d[x] for x in 'THREE')) % 3 == 0:
            print('HUIT = ', int(''.join(d[x] for x in 'HUIT')))

from itertools import permutations

# return a list of primes up to but not including n

def prime_list(n) :

sieve = [False, False] + [True] * (n - 1)

for i in range(2, int(n ** 0.5) + 1):

if sieve[i] :

m = n // i - i

sieve[i * i : n + 1 : i] = [False] * (m + 1)

return [ i for i in range(n + 1) if sieve[i] ]

pr = prime_list(2000)

# TWO + TWO = FOUR makes F = 1 and E is 3, 7 or 9

# because it is last digit of a four digit prime

for e in ('3', '7', '9'):

# permute the remaining digits and put them in the map

for p in permutations(set('023456789') - set((e,))):

d = dict(zip('THIORUVWEF', p + ((e, '1'))))

# check that T and H are not zero

if '0' not in p[:2]:

# check that FIVE is prime

five = int(''.join(d[x] for x in 'FIVE'))

if five in pr:

# check FIVE - TWO is prime and TWO + TWO = FOUR

two = int(''.join(d[x] for x in 'TWO'))

four = int(''.join(d[x] for x in 'FOUR'))

if five - two in pr and two + two == four:

# check that THREE is a multiple of 3

if int(''.join(d[x] for x in 'THREE')) % 3 == 0:

print('HUIT = ', int(''.join(d[x] for x in 'HUIT')))

Geoff Rounce permalink

My code is similar, but slower, and gives all the variables:


from itertools import permutations

def is_prime(n):
  for x in range(2, int(n ** 0.5) + 1):
    if n % x == 0:
      return False
  return True

for p in permutations('0123456789', 10):
  ndict = dict(zip('TWOUFIVEHR', p))
  # check T,F,H are not zero
  if p[0] != '0' and p[4] != '0' and p[8] != '0':
    two = int(''.join(ndict[x] for x in 'TWO'))
    three = int(''.join(ndict[x] for x in 'THREE'))
    four = int(''.join(ndict[x] for x in 'FOUR'))
    five = int(''.join(ndict[x] for x in 'FIVE'))
    huit = int(''.join(ndict[x] for x in 'HUIT'))
    # define teaser conditions
    if (two + two == four and is_prime(five) and 
        is_prime(five - two) and three % 3 == 0):
      print('two, three, four, five, huit = ', 
             two, three, four, five, huit)

from itertools import permutations

def is_prime(n):

for x in range(2, int(n ** 0.5) + 1):

if n % x == 0:

return False

return True

for p in permutations('0123456789', 10):

ndict = dict(zip('TWOUFIVEHR', p))

# check T,F,H are not zero

if p[0] != '0' and p[4] != '0' and p[8] != '0':

two = int(''.join(ndict[x] for x in 'TWO'))

three = int(''.join(ndict[x] for x in 'THREE'))

four = int(''.join(ndict[x] for x in 'FOUR'))

five = int(''.join(ndict[x] for x in 'FIVE'))

huit = int(''.join(ndict[x] for x in 'HUIT'))

# define teaser conditions

if (two + two == four and is_prime(five) and

is_prime(five - two) and three % 3 == 0):

print('two, three, four, five, huit = ',

two, three, four, five, huit)

Sunday Times Teaser 2605 – Simple Sums

by Graham Smithers

Published: 26 August 2012 (link)

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