Sunday Times Teaser 2517 – No Title

by Andrew Skidmore

Published December 19 2010 (link)

Finley is excited about Christmas. At school, he has made a card showing a triangular-shaped Christmas tree with a fairy on top. With this in mind, please decipher XMAS + TREE = FAIRY, where different letters stand consistently for different digits, and where TREE is a triangular number (ie, is the sum of some consecutive integers from 1 upwards).

What number is XMAS?

2 Comments Leave one →

Brian Gladman permalink

Using the alphasum.py:


from alphasum import AlphaSum

c = AlphaSum(['XMAS', 'TREE'], 'FAIRY')
for s in c.solve():
  t = 8 * int(c.substitute('TREE')) + 1
  if int(t ** 0.5) ** 2 == t:
    print(c.output())

from alphasum import AlphaSum

c = AlphaSum(['XMAS', 'TREE'], 'FAIRY')

for s in c.solve():

t = 8 * int(c.substitute('TREE')) + 1

if int(t ** 0.5) ** 2 == t:

print(c.output())

GeoffR permalink


from itertools import permutations
digits = set(range(10))

# from a list of 4-digit triangular numbers
tri4 = [n * (n + 1)// 2 for n in range(45,141)]

for p1 in permutations(digits,3):
  t, r, e = p1
  if t == 0: continue
  tree = 1000*t + 100*r + 11*e

  # check TREE is a triangular number
  if tree not in tri4: continue
    
  # permute remaining digits for XMAS and FAIRY
  qs = digits.difference(p1)
  for p2 in permutations(qs,7):
    x, m, a, s, i, f, y = p2
    if x == 0 or f == 0: continue
    xmas = 1000*x + 100*m + 10*a + s 
    fairy = 10000*f + 1000*a + 100*i + 10*r + y
    
    if xmas + tree == fairy:
      print(f'{xmas} + {tree} = {fairy}')
      print(f'XMAS = {xmas}')

from itertools import permutations

digits = set(range(10))

# from a list of 4-digit triangular numbers

tri4 = [n * (n + 1)// 2 for n in range(45,141)]

for p1 in permutations(digits,3):

t, r, e = p1

if t == 0: continue

tree = 1000*t + 100*r + 11*e

# check TREE is a triangular number

if tree not in tri4: continue

# permute remaining digits for XMAS and FAIRY

qs = digits.difference(p1)

for p2 in permutations(qs,7):

x, m, a, s, i, f, y = p2

if x == 0 or f == 0: continue

xmas = 1000*x + 100*m + 10*a + s

fairy = 10000*f + 1000*a + 100*i + 10*r + y

if xmas + tree == fairy:

print(f'{xmas} + {tree} = {fairy}')

print(f'XMAS = {xmas}')

Sunday Times Teaser 2517 – No Title

by Andrew Skidmore

Leave a Reply Cancel reply

Recent Posts

Recent Comments

Archives

Categories

Meta