Sunday Times Teaser 2808 – Hot Stuff

by Nick MacKinnon

Published: 17 July 2016 (link)

George and Martha are dabbling in the world of high temperature physics. George was measuring the temperature of a molten metal and wrote down the result. He thought this was in degrees Centigrade and so he converted it to Fahrenheit. However, Martha pointed out that the original result was already in degrees Fahrenheit and so George converted it to Centigrade. Martha wrote down the original result and each of George’s two calculated answers. She noted that they were all four-figure numbers and that their sum was palindromic.

What was the original four-figure result?

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Brian Gladman permalink


# The original temperature has to be of the
# form 1040 + 45 * k for integer k in order 
# to give integer converted values
for t in range(1040, 10000, 45):
  # convert to Fahrenheit
  f = 9 * t // 5 + 32
  if 1000 <= f < 10000:
    # convert the result to Centigrade
    c = 5 * (t - 32) // 9
    if 1000 <= c < 10000:
      # check for a sum of the three that
      # is a palindrome
      sm = str(t + c + f)
      if sm == sm[::-1]:
        print(t, (c, f, int(sm)))

# The original temperature has to be of the

# form 1040 + 45 * k for integer k in order

# to give integer converted values

for t in range(1040, 10000, 45):

# convert to Fahrenheit

f = 9 * t // 5 + 32

if 1000 <= f < 10000:

# convert the result to Centigrade

c = 5 * (t - 32) // 9

if 1000 <= c < 10000:

# check for a sum of the three that

# is a palindrome

sm = str(t + c + f)

if sm == sm[::-1]:

print(t, (c, f, int(sm)))

Here are two alternatives based on various amounts of prior analysis:


from itertools import count

# start with the last (Centigrade) value and
# convert to Fahrenheit twice; choose values
# for c such that the two Fahrenheit values
# are both (four digit) integers
for c in count(1010, 25):
  f = 9 * c // 5 + 32
  ff = 9 * f // 5 + 32
  # exit when the largest value has 5 digits
  if ff >= 10000:
    break
  # the sum of the 3 values is a palindrome
  sm = str(c + f + ff)
  if sm == sm[::-1]:
    print(f, (c, ff, int(sm)))

from itertools import count

# start with the last (Centigrade) value and

# convert to Fahrenheit twice; choose values

# for c such that the two Fahrenheit values

# are both (four digit) integers

for c in count(1010, 25):

f = 9 * c // 5 + 32

ff = 9 * f // 5 + 32

# exit when the largest value has 5 digits

if ff >= 10000:

break

# the sum of the 3 values is a palindrome

sm = str(c + f + ff)

if sm == sm[::-1]:

print(f, (c, ff, int(sm)))

and:


from itertools import count

# Start with the last (Centigrade) value as
# 1010 + 25.k; calculate the two Fahrenheit
# values and the sum of the three as:
#
#   c   = 1010 +  25.k
#   f1  = 1850 +  45.k
#   f2  = 3362 +  81.k
#   sum = 6222 + 151.k

for k in count():
  sm = 6222 + 151 * k
  # check for a palindrome
  if sm == int(str(sm)[::-1]):
    c  = 1010 + 25 * k
    f1 = 1850 + 45 * k
    f2 = 3362 + 81 * k
    print(f1, (c, f2, sm))
    break

from itertools import count

# Start with the last (Centigrade) value as

# 1010 + 25.k; calculate the two Fahrenheit

# values and the sum of the three as:

# c = 1010 + 25.k

# f1 = 1850 + 45.k

# f2 = 3362 + 81.k

# sum = 6222 + 151.k

for k in count():

sm = 6222 + 151 * k

# check for a palindrome

if sm == int(str(sm)[::-1]):

c = 1010 + 25 * k

f1 = 1850 + 45 * k

f2 = 3362 + 81 * k

print(f1, (c, f2, sm))

break

Sunday Times Teaser 2808 – Hot Stuff

by Nick MacKinnon

Published: 17 July 2016 (link)

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