Logic Problem

A test consists of 30 true or false questions. After the test (answering all 30 questions), Victor gets his score: the number of correct answers. Victor is allowed to take the test (the
same questions ) several times. Can Victor work out a strategy that insure him to get a perfect score after the 25th attempt?

have fun /sci/

Do your own homework

I solved it already >_<
It was fun :)

done
where'd you find problems like this? moar prz

>>1
Victor who?

Your logic already fails; logic is neither true nor false, only valid or invalid to see if said argument is worthy of further investigation.

It's Logical Captain


































































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It's Logical Captain

It's Logical Captain

It's Logical Captain

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It's Logical Captain

The question is from a international mathematics competition.
link here: http://www.math.toronto.edu/oz/turgor/
Go to archives section.
This question is from Senior A level of spring 2008.

He goes true true true with all questions, then, on every subsequent attempt, he switches one with false, and sees if the score changes.

>>14
Probably more effective to switch two at a time.

Reminds me of the coloured peg game Mastermind.

>>14
>>15
I'm original poster btw.

WOW! FAIL!
That would instantly result in 30 att (2 same{unless post processing <hint>})
YOU IDIOTS!

There are several outcomes dependent on chance.

If you are guessing, and you are allowed any way to answer and finish the test, but you must consider each question each time, and the questions are randomized, and you cannot understand the question, then the maximum amount of possible answers at any single instance is 265,252,859,812,191,058,636,308,480,000,000.

The maximum amount of time to ensure that it takes place, if no one is keeping track of their answer, is 70,359,079,638,545,882,374,689,246,780,656,000,000,000,000,000,000,000,000,000,000,000 attempts.

Although anyone with a lick of intelligence can solve this problem in 2 attempts.

The answer is yes.

I'm interested in >>18's surefire 2 attempt solution.  Here's mine, modified for twelve fixed questions in the example.

1. Set the first half of the problems false and the second half of the problems true; if the answer is less than half correct, switch them around.
2-x. Over a period of tests, change answers in both the first half and the second half of the test then submit.
: If the correct result count goes down, both original values are correct.
: If the count goes up, both of the new values are correct.
: If the count stays the same, only one of those new values was correct and you can figure out which by process of elimination:
In the following case, in step 1, only one is correct; in step 2, keeping the first one the same proves that the second is false.
A T || T   T
B F || T   F
C T ||     T
In the following case, in step 1, only one is correct; in step 2, we have one correct, which means A and B are still both false a C is correct (if we had have none correct, all the answers would be inverted).
A F || T   T   F
B T || T   F   T
C T ||     T   T
In the following case, in step 1, only one is correct; in step 2, keeping the first value the same only equals one more correct result; this means we know C is actually false.
A T || T   T   T
B F || T   F   F
C F ||     T   F

Example:
0    1   2       3   4   5   6   7   8
T || F   T  -F- -T-  T   T   T   T   T
T || F   T   T  -F-  T   T   T   T   T
F || F   T   T   T  -F-  F   F   F   F
T || F   T   T   T   T  -F-  T   T   T
F || F   T   T   T   T   T  -F- -F-  F
F || F   T   T   T   T   T   T  -F-  F
T || T   F  -T- (T)  T   T   T   T   T
T || T   F   F   F  -T-  T   T   T   T
F || T   F   F   F   F  -T-  F   F   F
F || T   F   F   F   F   F  -T- (T)  F
F || T   F   F   F   F   F   F   F   F
F || T   F   F   F   F   F   F   F   F
Note: -#- means the value has changed, (#) means this number was unchanged and is being tested this turn; by step 7, we have verified all 5 true values and solved the test in submission 8 (confirmation in 7/12 time, success in 2/3 time, less than 5/6 time).

This example forces us to test our numbers every other turn until we have verified the full first half:
0    1   2   3   4   5   6   7   8   9  10
T || T  -F- -T-  T   T   T   T   T   T   T
F || T   T  -F-  F   F   F   F   F   F   F
T || T   T   T  -F- -T-  T   T   T   T   T
F || T   T   T   T  -F-  F   F   F   F   F
T || T   T   T   T   T  -F- -T-  T   T   T
F || T   T   T   T   T   T  -F-  F   F   F
T || F  -T- (T)  T   T   T   T   T   T   T
F || F   F   F  -T- (T)  F   F   F   F   F
T || F   F   F   F   F  -T- (T)  T   T   T
F || F   F   F   F   F   F   F  -T-  F   F
F || F   F   F   F   F   F   F   F  -T-  F
T || F   F   F   F   F   F   F   F   F   T
We get our answer in 5/6 time the worst case example.

>>19
In that first example, step 2 was over the wrong column.  The column it is over depicts (mentally) switching around the half of the test that is more true and the half that is more false.  There is no test submission.

cheat on the 25th try

One shower later and I got this:

A: set them all to true or false; if less than half the answers are correct, invert all answers before proceeding.
(1) work only with the first/next six values
(2) invert the first two values.  If the correct number increases, keep the changes; if it decreases, change them back and proceed to the next two.  If you only have one correct, keep one answer changed, restore the other, and change the next question's answer, then do (3).
(3) If you lost a correct answer, all three values must be inverted.  If correct answers do not change, only the value that did not change is correct.  If there is an increase of one correct answer, the original two values must be inverted and the third is correct.  If they are all correct, they are all correct as they are.

The maximum amount of submissions it would take to get through all six values is four turns (like so: first two, first three, next two, last three).  At that rate, it will only take 20 submissions to check all five six-problem groups.
1 init + 20 tests + 1 final submission = 22 tries
You will have submitted a verified solution for the 30-question test in 22 submissions at most.

Logic problem


Logic is an essential part of clear thinking because it helps us draw conclusions. It is often used in Mathematics. For example, if A and B are separate numbers and A = X, then logically, we know that B cannot equal X. However, you also use logic every day, for instance, when you conclude that a neighbour is wealthy because he has a new car. Logic helps you
reach a conclusion on the evidence provided. You may, of course, come to the wrong conclusion, as in the example of your neighbour, who may just be looking after the car for his superior.

Logic problems are amusing games where the evidence is strictly limited and precisely stated.

just say T to the 1st one, and F to the rests, then get a score.
just say F to the 1st one, and F to the rests, then get a score.
now you find the the 1st one T or F.
Do the 2nd to 30th, one by one.
QED

>>24
You're running afoul of an advanced principle in logic, which goes "A number between 30 and 60 is greater than 25".