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Question

A * [(B + C)(D - E) - F(G*H) ] / J = 10

Knowing that each variable is a unique, single-digit, nonzero number, and that C - B = 1, and H - G = 3, what is the number ABCDEFGHJ, where each letter is a digit? For example, if A = 4, B = 2, and C = 7, ABC would equal 427.

Answer 1

do your own work

Answer 2

3 Answers are possible
2 6 7 8 3 5 1 4 9
2 6 7 9 5 3 1 4 8
6 7 8 4 1 3 2 5 9

I dont know if it is a logical puzzle... else it can be solved by the following code

int a,b,c,d,e,f,g,h,j;
for(a=1;a<=9;a++)
{
for(b=1;b<=9;b++)
{if(a!=b)
for(c=1;c<=9;c++)
{if(b!=c&&c!=a)
for(d=1;d<=9;d++)
{if(c!=d&&d!=b&&d!=a)
for(e=1;e<=9;e++)
{if(d!=e&&e!=c&&e!=b&&e!=a)
for(f=1;f<=9;f++)
{if(e!=f&&f!=d&&f!=c&&f!=b&&f!=a)
for(g=1;g<=9;g++)
{if(f!=g&&g!=e&&g!=d&&g!=c&&g!=b&&g!=a)
for(h=1;h<=9;h++)
{if(g!=h&&h!=f&&h!=e&&h!=d&&h!=c&&h!=b&&h!=a)
for(j=1;j<=9;j++)
{if(h!=j&&j!=g&&j!=f&&j!=e&&j!=d&&j!=c&&j!=b&&j!=a)
if (a * ((b + c)*(d - e) - f*(g*h) ) == 10*j&&(c-b==1)&&(h-g==3))
{
System.out.println(a+" "+b+" "+c+" "+d+" "+e+" "+f+" "+g+" "+h+" "+j);
}

}
}
}
}
}
}
}
}
}

Answer 3

A=2,B=6,C=7,D=9,E=5,F=3,G=1,H=4,J=B
so...ABCDEFGHJ = 26,795,314
there is no I value in your equation!
2*[(6+7)(9-5) - 3*1*4] / 8 = 10
[(13*4) - 12] / 4 = 10
[52-12] / 4 = 10
40/4 = 10
10 = 10

YAY!!!whew

Answer 4

267953148
ABCDEFGHJ

2 * [(6+7)(9-5) - 3*1*4] / 8 = 10
2 * [(13*4) - 12] / 8 = 10
2 * [52-12] / 8 = 10
2 * 40/8 = 10
2 * 5 = 10

now can we go get pizza?

Answer 5

Either A or (B+C)(D-E)-F(G*H) must be a multiple of 5. Number theory.
B + C = odd
G + H = odd

Strategically I wouldn't want G to be big. There must be a few solutions.

Answer 6

why is the same question asked by so many people? this question has been answered many times before in the last day or so.

Answer 7

I know the answer, but if I told you then I would have to share my Neopoints prize with you! :)

Answer 8

uh... good luck.