IceFall
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First measure 4 vs 4 balls with 4 ball not being measured. (Times balance used: 1)
Possible outcomes:
1. Balance doesn't incline
2. Balance inclines to a side.
Solving 1:
All eight balls are standard meaning the odd ball is within the 4 previously not measured.
Measure 3 of the 8 known standard balls vs 3 out of the 4 balls not measured. (Times balance used: 2)
Possible outcomes:
1a. Balance doesn't incline
1b. Balance inclines.
Solving 1a:
If there is no difference that means that the ball left out of the group of 4 balls is the odd one.
To determine whether it is heavier or lighter just use another standard ball, and depending the outcome you can tell if the odd ball is heavier or lighter. (Times: 3)
Solving 1b:
Depending the outcome you can tell whether the odd ball is lighter of heavier. Measure 1v1 of the bunch that was odd (Times: 3). If there is no difference the ball not measured is the odd ball.
If there is a difference, you can deduce which one is the odd ball since you already know if the odd ball is either light or heavy.
Solving 2:
The balance with move to one side. Meaning that the side that weights more has a heavy ball OR the lighter bunch has a light ball. Which would will give us 4 standards balls (SB) (the ones not measured), 4 balls of the bunch that could have a heavy ball (HB) and 4 with a possible light ball (LB). Note that HBs can only contain a odd heavy ball and LBs can only contain a light odd ball and not viceversa.
Now measure 3 HB + 1 LB vs 4 SB, leaving 3 LB outside. (Times: 2)
Possible outcomes:
2a. There is no difference.
2b. It tilts toward the 4 SB
2c. It tilts toward the 3 HB + 1 LB.
Solving 2a:
No difference, meaning that the odd ball is within the 3 LBs not measured. Measure 1v1 of those 3 leaving one out (Times: 3). If there is no difference then that one out is the light ball.
If there is a difference, whichever ball is recorded to be lighter than the other is the odd ball.
Solving 2b:
If the balance tilts toward the 4 SB, it means that the LB from the 3 HB + 1 LB is the odd one. Since only the LB could be a light odd ball. Thus making the 4 SB heavier.
Solving 2c:
If it balances toward the 3 HB + 1 LB. Then the LB is a actually a SB since only the 3 HB could be an odd heavy ball. Use the same method as in (2a) but instead look for the heavy ball. (Times: 3)
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I did this long time ago, don't remember the time. But probably around 5 to 10 minutes.
Most of you if not all probably got the wrong answer. If this puzzle is supposed to be solvable only for 2% of the population, then why is it that most people solved it and under 30 minutes? That is because they don't know they're wrong, they just think they got the right answer. It is not that hard to create a matrix and use linear logic to "solve" the puzzle, it doesn't take a genius to do that. If you said the German had the fish then you are wrong. Think about the last step you took to solve the puzzle. Are you sure that is logical?
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The fundamental flaw of the scientific method
in General Philosophy
Posted
A very interesting topic.
Sorry if my response is not a direct response to previous comments but there were too many walls of text and some of it were off-topic. (
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It is true that the scientific method, just like WHR said, has a flaw, but I would not call it "fundamental" but rather a pragmatic flaw.
As you may know the scientific method is a combination of inductive and deductive reasoning (the so called hypothesis + experimentation procedure). However, this means that the scientific method has some limitations to it. First, the scientific method is constrained by our technology. A caveman, no matter how incredibly intelligent he is, wouldn't be able to discover a quark since he doesn't have the technology to do it. Second, the scientific method is based upon statistical error and trial, and thus it can never prove something to be true. Heck, it can give us a very close answer but it is not necessarily the complete truth yet.
To illustrate this I will use the example of Galilean vs Relativistic transformations.
Galilean transformations is the common method to add velocities that we still use today for non-relativistic velocities. We now know that Galileo did not see the complete truth since we now know about Special relativity and the Lorenz factor. The reason Galileo would have never come up with this relativity is because he ever imagined there was a speed limit, nor had he a need to look for it. There was no need since relativistic speeds can't be seen on the Earth and thus his calculation were perfectly correct for that time.
Here is the flaw. Galilean transformations were considered to be truth since no one could defy his calculations since there was no experimental evidence to disprove him at the time. However, as we got deeper knowledge of light and relativity, we were able to disprove him. The scientific method bases its knowledge on "Working Models" and not necessarily truths. This means that scientific method can give us theories but not truths. It can only be disproved and never used to prove.
However, this flaw is not necessarily bad since we can use it to disprove previous theories and make them more complete just like the example.