CRAP!
That looks NOTHING like I remember. I can follow part of that but it gives me a headache
There must be another way or at least a simplification.
That looks NOTHING like I remember. I can follow part of that but it gives me a headache
There must be another way or at least a simplification.
There must be a better solution than that, its too complex. I didn't even understand a thing from that, why abcd=711000000
Does anyone else have another solution for this?
Does anyone else have another solution for this?
cgtran, abcd = 711000000 because
he converted from $1 to 100 cents.
Remember that EACH a, b, c, and d are multiplied
by 100. Thus original abcd is multiplied by
100000000 (or multiplied by 100 for 4 times).
he converted from $1 to 100 cents.
Remember that EACH a, b, c, and d are multiplied
by 100. Thus original abcd is multiplied by
100000000 (or multiplied by 100 for 4 times).
LOL
I'm not sure if it's because this DR.guy has overcomplicated his answer or maybe it was presented to me differently, but we also had the benefit of being able to yell questions as they came up, which sure beats seeing it written down!
br0wn seems to be onto it though...is there an easier way?
I'm not sure if it's because this DR.guy has overcomplicated his answer or maybe it was presented to me differently, but we also had the benefit of being able to yell questions as they came up, which sure beats seeing it written down!
br0wn seems to be onto it though...is there an easier way?
Alright! I came here to learn why my Netgear FT 711 doesn't work. And I didn't have to search long. Just kidding. Always enjoyed brainteasers.
I came pretty close just using a straight mean approach , although it's not perfect, it would work at any 7-11. lol
1.07
1.08
2.49
2.47
1.07
1.08
2.49
2.47
i still dont get why
ABCD = 711000000
but then that is not true
ABCD <> $71100000.00
<> means not equal to
ABCD = 711000000
but then that is not true
ABCD <> $71100000.00
<> means not equal to
(A * 100) * (B * 100) * (C * 100) * (D * 100) = A*B*C*D*100000000 so there is where those added 0's are coming from...
yes i know that is how you get the extra zeros
however, it DOES NOT MAKE SENSE TO DO IT
if you have
ABCD = 71100000000
then that means
multiplication of ABCD = 71100000000cents --> $711000000.00 DOLLARS
which is conflicting with the original given information
multiplication of ABCD does NOT means 71100000000cents, does NOT means $711000000.00 dollars
it is GIVEN to us that the multiplication of
ABCD = $7.11
you CANNOT suddently multiply the RHS with 100000000 but NOT the LHS
we CAN have
100000000ABCD = 71100000000cents
or
100000000ABCD = $711000000.00 dollars
we cannot have
ABCD = 7110000000cents
that is what i dont understand
however, it DOES NOT MAKE SENSE TO DO IT
if you have
ABCD = 71100000000
then that means
multiplication of ABCD = 71100000000cents --> $711000000.00 DOLLARS
which is conflicting with the original given information
multiplication of ABCD does NOT means 71100000000cents, does NOT means $711000000.00 dollars
it is GIVEN to us that the multiplication of
ABCD = $7.11
you CANNOT suddently multiply the RHS with 100000000 but NOT the LHS
we CAN have
100000000ABCD = 71100000000cents
or
100000000ABCD = $711000000.00 dollars
we cannot have
ABCD = 7110000000cents
that is what i dont understand
In order for the soultion given to work, each term on the LHS has to be multiplied by 100.
Because there are 4 terms on the LHS, the RHS must be multiplied by 10^8.
By multipliying each term on the LHS, you are changing the question to 'what 4 integers when added equal 711, but when multiplied equal 711000000?' This is a sound method of solving this problem.
Because there are 4 terms on the LHS, the RHS must be multiplied by 10^8.
By multipliying each term on the LHS, you are changing the question to 'what 4 integers when added equal 711, but when multiplied equal 711000000?' This is a sound method of solving this problem.
Given: ABCD = $7.71
you guys say
ABCD = 77100000000cents
therefore
ABCD = $771000000.00 <- this contradicts to what is given
as someone pointed out
100000000ABCD = 77100000000 cents <-this IS correct
but cancelling out 100000000
you again end up with
ABCD = $7.71
not ABCD = 77100000000
this is why i dont get it
you guys say
ABCD = 77100000000cents
therefore
ABCD = $771000000.00 <- this contradicts to what is given
as someone pointed out
100000000ABCD = 77100000000 cents <-this IS correct
but cancelling out 100000000
you again end up with
ABCD = $7.71
not ABCD = 77100000000
this is why i dont get it
Argle we're using the variables to mean 2 thinks.
Okay we're told ABCD=$7.11
He wants to change it to all cents
so you work it out and get ABCD=711000000
The variables are not equal. A in the first equation is a dollar amount, A in the 2nd equation is in cents.
More clearly he coulda written
abcd=7.11
A=100a
B=100b
C=100c
D=100d
(A/100)(B/100)(C/100)(D/100)=7.11
ABCD/100000000=7.11
ABCD=711000000
A and a are NOT equal
Okay we're told ABCD=$7.11
He wants to change it to all cents
so you work it out and get ABCD=711000000
The variables are not equal. A in the first equation is a dollar amount, A in the 2nd equation is in cents.
More clearly he coulda written
abcd=7.11
A=100a
B=100b
C=100c
D=100d
(A/100)(B/100)(C/100)(D/100)=7.11
ABCD/100000000=7.11
ABCD=711000000
A and a are NOT equal
xtreme2k, if you still don't get it, here is a little
example :
Suppose you have 2 numbers, A and B in dollars.
A+B = $4
A*B = $4
One solution is A and B are both $2.
Now if we change this into cents :
A = 200 cents
B = 200 cents
A+B = 400 cents which is still $4
BUT
A*B = 200 * 200 = 40000 which is not $4
What happened ?
When you convert the Left side of A*B, you multiplied
both A and B by 100.
Thus the right side need to be multiplied by 100^2, not by 100
only.
THUS you can't change the equation of
A*B = $4
into cents
like the following :
A*B = 400 cents
It should be :
A*B = 40000 cents
Regarding the solution from the site
It is quite simple, it is based on 1 fact,
which is the geometric mean.
Since we only have 2 equations and there are 4 unknowns, we need
to find some other informations (this is where the info about
geometric mean comes).
What is geometric mean ?
"The geometric mean" of 2 number, A and B is the
square root of A*B
for 3 number, A, B and C, is the
cube root of A*B*C
and soon
"Arithmetic mean" on the other hand, sum all the numbers
and divide by how many numbers there are.
One fact to explore of geometric mean is that it is NEVER larger
than the arithmetic mean.
Thus the solution from the net, exploit this fact.
Since we can find geometric mean and arithmetic mean of
the 4 numbers.
We are given A+B+C+D, thus dividing by 4 will give us
the arithmetic mean.
We are also given A*B*C*D, thus taking a quadruple root will
gives us the geometric mean.
Also the solution for that site, use a simple TRIAL and ERROR.
It knows that one of the number A must be a multiplicity of 79 (one
of the primes by factoring 711000000).
Thus it exploits this fact and come out with result that A = t*75,
where t must be from 1 to 4.
Knowing the range of A, it is easy use this fact and geometric fact to find
the other 3 numbers (note that we can find the geometric mean
and arithmetic mean from those 3 numbers). And if the geometric
mean is larger than arithmetic, it means that we are trying the
wrong number.
Thus using this TRIAL and error, it can produce a unique solution for
the 4 numbers.
example :
Suppose you have 2 numbers, A and B in dollars.
A+B = $4
A*B = $4
One solution is A and B are both $2.
Now if we change this into cents :
A = 200 cents
B = 200 cents
A+B = 400 cents which is still $4
BUT
A*B = 200 * 200 = 40000 which is not $4
What happened ?
When you convert the Left side of A*B, you multiplied
both A and B by 100.
Thus the right side need to be multiplied by 100^2, not by 100
only.
THUS you can't change the equation of
A*B = $4
into cents
like the following :
A*B = 400 cents
It should be :
A*B = 40000 cents
Regarding the solution from the site
It is quite simple, it is based on 1 fact,
which is the geometric mean.
Since we only have 2 equations and there are 4 unknowns, we need
to find some other informations (this is where the info about
geometric mean comes).
What is geometric mean ?
"The geometric mean" of 2 number, A and B is the
square root of A*B
for 3 number, A, B and C, is the
cube root of A*B*C
and soon
"Arithmetic mean" on the other hand, sum all the numbers
and divide by how many numbers there are.
One fact to explore of geometric mean is that it is NEVER larger
than the arithmetic mean.
Thus the solution from the net, exploit this fact.
Since we can find geometric mean and arithmetic mean of
the 4 numbers.
We are given A+B+C+D, thus dividing by 4 will give us
the arithmetic mean.
We are also given A*B*C*D, thus taking a quadruple root will
gives us the geometric mean.
Also the solution for that site, use a simple TRIAL and ERROR.
It knows that one of the number A must be a multiplicity of 79 (one
of the primes by factoring 711000000).
Thus it exploits this fact and come out with result that A = t*75,
where t must be from 1 to 4.
Knowing the range of A, it is easy use this fact and geometric fact to find
the other 3 numbers (note that we can find the geometric mean
and arithmetic mean from those 3 numbers). And if the geometric
mean is larger than arithmetic, it means that we are trying the
wrong number.
Thus using this TRIAL and error, it can produce a unique solution for
the 4 numbers.
MereMortal
Golden Member
- Oct 16, 2000
- 1,919
- 2
- 81
Much of the confusion here is because the statement of the problem is
incorrect.
If you have four items with units of dollars, then their sum will be
in dollars. If you take their product, however, the resulting unit
is not dollars, but dollars^4.
Then you can use the conversion
1 dollar^4 = (100 cents)^4 = 100000000 cents^4
to go about solving the problem.
Hope that helps. The surgeon general says units are important: ignoring them may cause your spacecraft to crash into Mars.
incorrect.
If you have four items with units of dollars, then their sum will be
in dollars. If you take their product, however, the resulting unit
is not dollars, but dollars^4.
Then you can use the conversion
1 dollar^4 = (100 cents)^4 = 100000000 cents^4
to go about solving the problem.
Hope that helps. The surgeon general says units are important: ignoring them may cause your spacecraft to crash into Mars.
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