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April 25th, 2014, 12:29 AM   #1
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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
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April 25th, 2014, 10:19 AM   #2
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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.
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April 25th, 2014, 10:32 AM   #3
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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.
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April 25th, 2014, 10:50 AM   #4
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Math Focus: सामान्य गणित
17 4 68 25 93
i dont understand the code
could you please explain
is it like hit and trial
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April 25th, 2014, 10:51 AM   #5
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Those are the 2-, 1-, 2-, 2-, and 2-digit numbers you asked for, I believe.
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April 25th, 2014, 11:03 AM   #6
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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 ?
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April 25th, 2014, 11:58 AM   #7
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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} $

Thanks from Olinguito
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April 25th, 2014, 12:08 PM   #8
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so i can't solve it by equations !!
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April 25th, 2014, 12:39 PM   #9
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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:

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


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

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April 25th, 2014, 12:43 PM   #10
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Math Focus: सामान्य गणित
same alphabet = same digit ?
i'll try to solve them till tomorrow
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