Sunday Times Teaser 2563 – Prime Time

by Andrew Skidmore

Published: 6 November 2011 (link)

In this addition sum I have consistently replaced digits by letters, with different letters for different digits, and I have ended up with another correct addition sum.

O N E
T W O
F I V E
=========
E I G H T

What is the prime number NOW?

2 Comments Leave one →

Brian Gladman permalink

This is easy with my AlphaSum alphametic sum solver and my number theory library:


from alphasum import AlphaSum
from number_theory import is_prime

c = AlphaSum(['ONE', 'TWO', 'FIVE'], 'EIGHT')
for r in c.solve():
  now = int(''.join(str(r[x]) for x in 'NOW'))
  if is_prime(now):
    print('NOW = {} ({}).'.format(now, c.output(r)))

from alphasum import AlphaSum

from number_theory import is_prime

c = AlphaSum(['ONE', 'TWO', 'FIVE'], 'EIGHT')

for r in c.solve():

now = int(''.join(str(r[x]) for x in 'NOW'))

if is_prime(now):

print('NOW = {} ({}).'.format(now, c.output(r)))

geoffrounce permalink

I tried a two stage permutation, finding ONE, TWO and NOW in the first stage and FIVE and EIGHT in the second stage.


from number_theory import is_prime
from itertools import permutations

for p1 in permutations('9876543210',5):
  O, N, E, T, W = p1
  if O == '0' or T == '0' or E == '0' or N == '0' : continue
  if not is_prime(int(N + O + W)): continue
  ONE, TWO = int(O + N + E), int(T + W + O)
  
  p2 = set('1234567890').difference(p1)
  for q in permutations(p2,5):
    F, I, V, G, H  = q
    if F == '0': continue
    FIVE, EIGHT = int(F + I + V + E), int(E + I + G + H + T)
    if ONE + TWO + FIVE == EIGHT:
      print('NOW =', int(N + O + W))
      print('ONE={}, TWO={}, FIVE={}, EIGHT={}'.format(ONE,TWO,FIVE,EIGHT))

from number_theory import is_prime

from itertools import permutations

for p1 in permutations('9876543210',5):

O, N, E, T, W = p1

if O == '0' or T == '0' or E == '0' or N == '0' : continue

if not is_prime(int(N + O + W)): continue

ONE, TWO = int(O + N + E), int(T + W + O)

p2 = set('1234567890').difference(p1)

for q in permutations(p2,5):

F, I, V, G, H = q

if F == '0': continue

FIVE, EIGHT = int(F + I + V + E), int(E + I + G + H + T)

if ONE + TWO + FIVE == EIGHT:

print('NOW =', int(N + O + W))

print('ONE={}, TWO={}, FIVE={}, EIGHT={}'.format(ONE,TWO,FIVE,EIGHT))

Sunday Times Teaser 2563 – Prime Time

by Andrew Skidmore

Published: 6 November 2011 (link)

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