Please help me with this equation... can't solve it

[kee2ka4]

What initial values of a and c are required such that the final values of a and b are:

a = 32
b = 4

…

int a,b,c

a = ?
b = 0
c = ?

for( b=0; a<12; b++ )
{
a = (a+a) * c;
}


I have tried working it out but at loop 3 (b=3) I keep getting the value of a as 16 which is greater then 12. This is when I assume that a is 1 and c is 1 but it doesn't work.

Any help appreciated.

Kind Regards

[rsrinivasan]

What initial values of a and c are required such that the final values of a and b are:

a = 32
b = 4

…

int a,b,c

a = ?
b = 0
c = ?

for( b=0; a<12; b++ )
{
a = (a+a) * c;
}


I have tried working it out but at loop 3 (b=3) I keep getting the value of a as 16 which is greater then 12. This is when I assume that a is 1 and c is 1 but it doesn't work.

Any help appreciated.

Kind Regards

Hi,
The final value of a=32 and b=4, when a=32 and c=1. But one condition you should change the for loop condition as "a<17" instead of "a<12".

Thanks,
Srinivasan r.

[Ganon11]

I think the problem is that the only values kee2ka4 can choose are a and c - the loop, conditions, expressions, and final results cannot be manipulated.

[JosAH]

Hi,
The final value of a=32 and b=4, when a=32 and c=1. But one condition you should change the for loop condition as "a<17" instead of "a<12".

That's cheating! ;-) There's no need to change that loop condition.
Here's the problem again:

a = 32
b = 4
 
…
 
int a,b,c
 
a = ?
b = 0
c = ?
 
for( b=0; a<12; b++ )
{
   a = (a+a) * c;
}

The final value of a == 32. So the expression (a+a)*c= 2*a*c must be a power
of two (because 32 is a power of two). So a*c must be a power of two. Every
value of a_n == 2^n*a_0*c^n where a_0 is the initial value of a and a_n is the
last value of a (== 32).

2^(n-1)*a_0*c^(n-1) should be less than 12 (by the condition), so 2*c should be
at least equal to 4 (c in [2, 4, 8, 16]) and the accompanying values of a are
in [8, 4, 2, 1].

kind regards,

Jos

[jaiminpsoni]

The answer is

a=2
c=-1