Hey, this is Presh Talwalkar
Catherine asks, "How many fish did you catch?"
Barney says, "I caught five."
Alfred says, "I caught two."
Barney then says,
"Don't listen to Alfred. You have to multiply any number he speaks aloud by six to get the real value."
Alfred then says, "Don't listen to Barney."
"You have to subtract two from any number he speaks aloud to get the real value."
Catherine knows
Alfred always speaks aloud a number equal to the real number divided by some constant and
Barney always speaks aloud a number equal to the real number plus
some fixed value
Catherine after thinking it over says "I know how many fish each of you actually caught."
How many fish did Barney actually catch, and how many did Alfred actually catch?
I thank Halvor Kjærås for creating this problem and sending me its solution. It has a very unique
mechanism out of logic puzzles that I have presented.
Can you figure it out? Give this problem a try and when you're ready keep watching the video for the solution.
So at first the problem seems easy.
But if it seems easy to you, you might be falling for the tempting but wrong answer.
You might think that
Alfred, every number he says you have to multiply by six
So if Alfred says he caught two fish that means he caught two times six which equals 12 fish.
Similarly
from Barney's number you might think you have to deduct two from the number
he speaks
So if Barney says he caught five fish you might think he actually caught five minus two which equals three fish
But this is the incorrect answer
The problem is that Barney adds a constant to every number spoken aloud
So even the claim of six is not the true value
That number six has also been modified by the number he adds to spoken numbers.
Similarly
Alfred divides by a value before speaking a number aloud so the claim of two is also not correct.
So before you figure out how many fish each person caught we have to figure out the correct
'fibbing values' of each person.
How do we do that?
Let's suppose that 'a' is the factor to multiply
Alfred spoken numbers to get the true value, this is Alfred's 'fibbing factor' and
And let's say B is the constant to deduct from Barney's spoken numbers to get the true value or
Barney's 'fibbing factor'
Now Barney says that Alfred's 'fibbing factor' is six
So we write this that Barney speak 6 equals Alfred's 'fibbing factor'
Now we have to adjust the number six by Barney's 'fibbing factor', so 6 minus B
Is the real value of Alfred's 'fibbing factor'
Alfred's 'fibbing factor' is equal to 'a'
so we have six minus 'B' as equal to 'a'
Now Alfred says that Barney's 'fibbing factor' is 2
So if Alfred speaks that 2 is equal to Barney's fibbing factor
We have to modify that number too, so we have 2 times a is the real value for Barney's fitting factor
therefore 2 'a'
equals B. Which is Barney's 'fibbing factor'
So we now have a system of two equations in two variables
6 minus B is equal to 'a' and 2 a equals B
We can use the second equation and substitute it into the first so we have B equals 2a
therefore 6 minus 2a is equal to 'a'
Which then means 6 is equal to 3a, or 'a' is equal to 2
since B is equal to 2a that means B is equal to 4, so we
solved for the fibbing factor of each person
We know that we have to multiply
Alfred's spoken numbers by 2
to get the true value. And we have to deduct 4 from Barneys spoken numbers to get the true value
So when Barney says he caught five fish,
That means he actually caught 5 minus 4 which equals one fish
When Alfred says he caught two fish
He actually caught 2 times 2 which equals four fish, and that's the correct answer.
Did you figure it out?
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