Sunday Times Teaser 2748 – I Go Up and Up

by Victor Bryant

Published: 24 May 2015 (link)

I have in mind an arithmetic progression; ie, a sequence which goes up and up by a fixed amount (such as 1, 10, 19, 28, …) and — as in that example — one of the terms of my progression will eventually be 10000. But I have coded the numbers by consistently replacing digits by letters and in this way the arithmetic progression has become

I, GO, UP, AND, …

To win a few pounds, please send in the number POUND.

2 Comments Leave one →

Brian Gladman permalink


# I is a single digit number
for I in range(10):
  # UP has two digits
  for up in range(10, 100):
    # check that GO is a two digit integer
    go, r = divmod(I + up, 2)
    # and that the sequence includes 10000
    if r == 0 and go > 9 and not (10000 - I) % (go - I):
      # compute the sequence increment and the letter's digits
      inc, (U, P), (G, O) = go - I, str(up), str(go)
      s1 = set([str(I), G, O, U, P])
      # check that the digits are all different
      if len(s1) == 5:
        # extract AND and ensure that its digits are different
        str_and = str(I + 3 * inc)
        s2 = set(str_and) 
        if len(str_and) == len(s2) == 3:
          A, N, D = str_and
          # ensure all the letters are different and A > 0  
          if not (A == '0' or s1 & s2):
            print('POUND is {}'.format(P + O + U + N + D))

# I is a single digit number

for I in range(10):

# UP has two digits

for up in range(10, 100):

# check that GO is a two digit integer

go, r = divmod(I + up, 2)

# and that the sequence includes 10000

if r == 0 and go > 9 and not (10000 - I) % (go - I):

# compute the sequence increment and the letter's digits

inc, (U, P), (G, O) = go - I, str(up), str(go)

s1 = set([str(I), G, O, U, P])

# check that the digits are all different

if len(s1) == 5:

# extract AND and ensure that its digits are different

str_and = str(I + 3 * inc)

s2 = set(str_and)

if len(str_and) == len(s2) == 3:

A, N, D = str_and

# ensure all the letters are different and A > 0

if not (A == '0' or s1 & s2):

print('POUND is {}'.format(P + O + U + N + D))

geoffrounce permalink


from itertools import permutations

for q in permutations('1234567890',3):
  # find numbers I and GO 
  i,g,o = q
  if i == '0' : continue
  if g == '0' : continue
  I = int(i)
  GO = int(g + o)
  q1 = set('1234567890').difference(q)

  # find number UP
  for q2 in permutations(q1,2):
    u, p = q2
    if u == '0' : continue
    UP = int(u + p)
    # check differences are the same
    if GO - I == UP - GO:
      q3 = q1.difference(q2)

      # find number AND
      for q4 in permutations(q3,3):
        a, n, d = q4
        if a == '0' : continue
        AND = int(a + n + d)
        # check differences are the same
        if UP - GO == AND - UP:
          diff = UP - GO
          if (10000 - I) % diff == 0:
            POUND = int(p + o + u + n + d)
            print('POUND = ',POUND)

from itertools import permutations

for q in permutations('1234567890',3):

# find numbers I and GO

i,g,o = q

if i == '0' : continue

if g == '0' : continue

I = int(i)

GO = int(g + o)

q1 = set('1234567890').difference(q)

# find number UP

for q2 in permutations(q1,2):

u, p = q2

if u == '0' : continue

UP = int(u + p)

# check differences are the same

if GO - I == UP - GO:

q3 = q1.difference(q2)

# find number AND

for q4 in permutations(q3,3):

a, n, d = q4

if a == '0' : continue

AND = int(a + n + d)

# check differences are the same

if UP - GO == AND - UP:

diff = UP - GO

if (10000 - I) % diff == 0:

POUND = int(p + o + u + n + d)

print('POUND = ',POUND)

Sunday Times Teaser 2748 – I Go Up and Up

by Victor Bryant

Published: 24 May 2015 (link)

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