S2T2

Jim Randell 9:54 am on 10 August 2021 Permalink Reply
Tags: by: Danny Roth ( 84 )   

• 

  Jim Randell 9:57 am on 10 August 2021 Permalink | Reply

  This Python program considers possible 4-digit numbers for the first reading, and then looks for viable second and third numbers that give a palindromic sum. It runs in 55ms.

  Run: [ @replit ]

  from enigma import (div, irange, is_npalindrome, printf)
  
  # convert centigrade (celsius) to fahrenheit
  c2f = lambda n: div(9 * n + 160, 5)
  
  # convert fahrenheit to centigrade (celsius)
  f2c = lambda n: div(5 * n - 160, 9)
  
  # original number (a 4-digit number)
  for n1 in irange(1000, 9999):
  
    # second number
    n2 = c2f(n1)
    if n2 is None or n2 < 1000 or n2 > 9999: continue
  
    # third number
    n3 = f2c(n1)
    if n3 is None or n3 < 1000 or n3 > 9999: continue
  
    # look for a palindromic sum
    t = n1 + n2 + n3
    if is_npalindrome(t):
      # output solution
      printf("n1={n1} n2={n2} n3={n3} t={t}")
  

  Solution: The original reading was 3155.

  And:

  3155 °C = 5711 °F
  3155 °F = 1735 °C
  3155 + 5711 + 1735 = 10601

  ---

  With analysis we can restrict the numbers considered for n1, and simplify the calculations.

  We see n1 must be in the range [1832, 5537], and must be a multiple of 5, and must equal 5 (mod 9).

  Run: [ @replit ]

  from enigma import (irange, is_npalindrome, printf)
  
  # all three numbers have 4 digits
  for k in irange(41, 122):
    # original number
    n1 = 45 * k + 5
    # second number
    n2 = 81 * k + 41
    # third number
    n3 = 25 * k - 15
    # look for a palindromic sum
    t = n1 + n2 + n3
    if is_npalindrome(t):
      # output solution
      printf("n1={n1} n2={n2} n3={n3} t={t}")
  

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• 

  GeoffR 11:55 am on 10 August 2021 Permalink | Reply

  Checking for the palindromic sum was a bit lengthy in MiniZinc, as I could not be sure if this total was four or five digits long.

  
  % A Solution in MiniZinc 
  include "globals.mzn";
  
  % T1 = original temperature, T2 in F, T3 in C
  var 1000..9999:T1; var 1000..9999:T2; var 1000..9999:T3;
  
  var 1000..99999: T4; % total of three temperatures
  
  constraint 5 * (T2 - 32) == 9 * T1;  % T2 = C to F from T1
  
  constraint 9 * T3 == 5 * (T1 - 32);  % T3 = F to C from T1
  
  constraint T4 == T1 + T2 + T3;
  
  % check for a 4-digit or 5-digit palindrome sum for T4
  var 1..9:a; var 0..9:b; var 0..9:c; var 0..9:d; var 0..9:e;
  
  constraint (T4 < 10000 /\ a == T4 div 1000 /\ b == T4 div 100 mod 10
  /\ c == T4 div 10 mod 10 /\ d == T4 mod 10 /\ a == d /\ b == c)
  \/
  (T4 > 10000 /\ a == T4 div 10000 /\ b == T4 div 1000 mod 10
  /\ c == T4 div 100 mod 10 /\ d == T4 div 10 mod 10 /\ e  == T4 mod 10
  /\ a == e /\ b == d);
  
  solve satisfy;
  
  output ["Original Temperature = " ++ show(T1) ++ "\n"
  ++ "Conversion Temperatures = " ++ show(T2) ++ ", " ++ show(T3)
  ++ "\n" ++ "Palindromic sum of three temperatures = " ++ show(T4) ];
  
  % Original Temperature = 3155
  % Conversion Temperatures = 5711, 1735
  % Palindromic sum of three temperatures = 10601
  % ----------
  % ==========
  
  

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