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 April 25th, 2014, 12:29 AM #1 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 884 Thanks: 61 Math Focus: सामान्य गणित solve (10a + b)c = 10d + e (10 d + e) + (10f + g) = 10 h + i a <> b <> c <> d <> e <> f <> g <>h <> i 1 <= a, b, c, d, e, f, g, h, i >=9
 April 25th, 2014, 10:19 AM #2 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 884 Thanks: 61 Math Focus: सामान्य गणित description : there is a two digit number which is multiplied by a single digit number, the result is added to a two digit number to get another two digit number. If none of the digits in the number is be reapeted and none of the number contain the digit 0. find the numbers.
 April 25th, 2014, 10:32 AM #3 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Code: chk(v)=my(s="");for(i=1,#v,s=Str(s,v[i]));s=Vec(s);if(#s==#Set(s),print(v)) for(a=10,99,for(b=1,89\a,for(c=10,99-a*b,chk([a,b,a*b,c,a*b+c])))) gives Code: [17, 2, 34, 56, 90] [17, 4, 68, 25, 93] [18, 2, 36, 54, 90] [38, 2, 76, 14, 90] This is, of course, PARI/GP.
 April 25th, 2014, 10:50 AM #4 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 884 Thanks: 61 Math Focus: सामान्य गणित 17 4 68 25 93 i dont understand the code could you please explain is it like hit and trial
 April 25th, 2014, 10:51 AM #5 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Those are the 2-, 1-, 2-, 2-, and 2-digit numbers you asked for, I believe.
 April 25th, 2014, 11:03 AM #6 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 884 Thanks: 61 Math Focus: सामान्य गणित chk(v)=my(s="");for(i=1,#v,s=Str(s,v[i]));s=Vec(s);if(#s==#Set(s),print(v)) for(a=10,99,for(b=1,89\a,for(c=10,99-a*b,chk([a,b,a*b,c,a*b+c])))) i was telling the code above is it some kind of program to find the digits ? and if it is, dose the program find the digits by hit and trial ?
April 25th, 2014, 11:58 AM   #7
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Hello, MATHEMATICIAN!

Quote:
 Solve the alphametic: $\displaystyle \quad \begin{array}{cc} A & B \\ \times & C \\ \hline D & E \end{array}\qquad \begin{array}{ccc} & D & E \\ + & F & G \\ \hline & H & I \end{array}$

This requires some trial-and-error
$\displaystyle \;\;\;$and a lot of common sense.

$\displaystyle \quad \begin{array}{cc} 1 & 7 \\ \times & 4 \\ \hline 6 & 8 \end{array}\qquad \begin{array}{ccc} & 6 & 8 \\ + & 2 & 5 \\ \hline & 9 & 3 \end{array}$

 April 25th, 2014, 12:08 PM #8 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 884 Thanks: 61 Math Focus: सामान्य गणित so i can't solve it by equations !!
April 25th, 2014, 12:39 PM   #9
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Hello, MATHEMATICIAN!

Quote:
 so i can't solve it by equations!!

That's right.
I'd say all Alphametics require trial-and-error
$\displaystyle \quad$plus Thinking (logic, elimination, etc.)

Here are two classic problems:

$\displaystyle \quad\begin{array}{ccccc} & S&E&N&D \\ + & M&O&R&E \\ \hline M&O&N&E&Y \end{array}$

$\displaystyle \quad \frac{\text{EVE}}{\text{DID}} \:=\:\text{0.TALKTALK...}$

 April 25th, 2014, 12:43 PM #10 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 884 Thanks: 61 Math Focus: सामान्य गणित same alphabet = same digit ? i'll try to solve them till tomorrow

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