Step by step deduction
Some "easy" deductions (no lights around 0, lights in white squares surrounded by black, etc.) get us to here:
See that 1 in the fourth row, third column? I'm going to assume the light next to it is on the right, and then we can deduce as follows to get a contradiction:
In fact, that same contradiction would arise ...
As an example, say we have numbers 1, 2, 3. Then, we find the sum of the three numbers, which is six. Then, we take the numbers and lay them out in a row. Then, we ask the sum of two slips. Then, we ask for the sum of another two slips. The one with the greater sum has the biggest number in the group. The one with the smaller sum would have the smaller ...
Without restriction of only checking consecutive papers
The general solution for $n$ would be:
With condition of only checking consecutive papers
I believe this is the general equation for $n$:
For $n > 2$:
Maybe I missed the point here but surely if you used values 1,2,4,8,16....32768 you could tell which two values were selected in any pair, so you'd have at most 2 possibilities for each piece of paper. By mutual exclusion and 'walking' your way along you could identify each value. This would take 14 goes at most.
I can prove that
The difficulty comes in distinguishing each of the 14 pairs of neighboring slips of paper, as well as the first and last papers. There are 15 such pairs of slips of paper. If a question includes or excludes both slips, the response will be the same if those slips were swapped. In contrast, a question can only distinguish the ...
By choosing appropriate numbers to write at the start, you can manage it with
Choice of numbers
The numbers you should write at the beginning are
Let's label the numbers, in the new order as they're laid out face down, $a,b,c,d,e,f,g,h,i,j,k,l,m,n,o$.
Every time you ask a question about some subset of consecutive papers, you know
Note that ...
I don't know the whole answer, but my guess is that .......__.. is Morse Code. Unfortunately, due to a lack of spacing, there are many ways to translate it.
The next sentence says 'V is a sign for you.' This could mean to look for V in the code (..._). This translates as HVD, SEVD, ESVD, IIVD, EEIVD, EIEVD, IEEVD, EEEEVD, HVNE, SEVNE, ESVNE, IIVNE, EEIVNE,...
Step by step deduction
The ginger snaps placed higher than the cookies baked by Emerson, but lower than the cookies presented on the brown plate.
The cookies baked by Pepper placed directly below the sugar cookies.
The cookies presented on the silver plate placed directly above the cookies presented on the red plate. Belle did not present ...
Step by step deduction
Firstly, note that MASTERING is a full nine-letter word so it takes up a whole row, and EMIGRANT is an eight-letter word so the column is either EMIGRANTS or SEMIGRANT. Also note that ARTEMIS must begin from either the 1st or 3rd place in its row, because otherwise the A will clash with MASTERING; and the remaining ...
@ChrisSteinbeckBell - Because you haven't replied to the previous answer yet, I am not sure if you are fully comprehending the kind of logical reasoning needed to solve a problem like this.
What follows is not intended to be a complete answer to your question, but just a helpful tip.
When studying logic, it is extremely important to understand the ...
If there are no government subsidies for agriculture, then there are government controls on agriculture. If there are government controls on agriculture, then there is no agricultural depression. There is depression or agricultural overproduction. It is a fact that there is no overproduction. Indicate the true alternative.
A step by step approach would ...
From the fourth clue, the one who does athletics is friends with Phillip.
From your deductions so far, you know Phillip is the one who does swimming. That means, from the first clue, Phillip and Marina don't know each other.
Therefore Marina can't be the one doing athletics, because that one is Phillip's friend and she isn't. This excludes your second ...
The degree of friendship or acquaintance is not important except to show differences.
Lara and the graphics designer known each other. They are godmothers.
The photographer, Brenda and the graphics designer are married.
Mie and Lara enjoy always being without make up or any personal care or beauty treatments.
Nancy, the baker and the photographer don't ...
This is a variant of the classical two roads, two guards problem, except that
So the question should be:
The sentry has a habit of alternately speaking the truth and telling a lie, so:
If his answer now is the truth, then
If his answer now is a lie, then
Either way, you've got your answer
I can only uniquely determine the pair of dice that the friend rolled, but I am unable to determine conclusively which of those two dice he showed to the narrator, because the odds of guessing the other seem to me THE SAME in either case.
First, I believe that the rolled dice are:
My reasoning is as follows:
Just using directly the information given (ignoring more/less buttons for the moment, as we'll come back to that later, but using the information that more/less means not the same):
(In the pictures I'm using red fill for no and green fill for yes, just to make it easy for myself when filling the grid.)
Then we know
Starting over (I'm using the notation HS, as in 93 where 9 is hidden and 3 is shown):
If we operate on only one sentence at a time:
1A: "Well, either of my dice could only go on one card."
Then, you say: "That still isn't enough for me to know what your other die is,"
Your friend responds:
2: "Yeah, but if I had placed the other die, you would have said ...
Having twice arrived at the conclusion that the situation described in the puzzle is impossible, I've done it again extremely carefully and systematically. I reach the same conclusion, and at this point while I fully admit that I may be getting it wrong I think it's more likely that either I am misunderstanding the terms of the puzzle, or there's an actual ...
"Can the two logicians redeem themselves? If so, what will the reasoning behind the correct answer be, and what's the minimum number of days it will take either of them to answer correctly?"
[NOTE: This is flawed at this moment, I'll remove this note if I can fix it.]
Main Line of Logical Reasoning:
[This all occurs before any passing or answer.]
Your sister is
and the age on the cake is
Proof of uniqueness
We're given several pieces of information:
"transposed the digits of her age" - her age is 2 digits.
"She'll thank you for the compliment" - the age on the cake makes her seem younger, so the second digit is smaller than the first.
"her age is a prime number" - her age is a 2-digit ...
This puzzle is very difficult, or indeed impossible, until you work in the meta-knowledge:
But the puzzle explicitly says that the Anthropologist did gain information, which means that
In that case, the person that answered must surely be
After some trial and error, I think I got it now.
[Edit: @LannyStrack provides below the "classic" answer to this puzzle which
is more elegant, but I also like my solution and the symmetry in the question :-)]
I got A and here is my reasoning (of course, no guarantee it's correct or even CLOSE to the most logical solution):
Before we delve into the main explanation, let us establish these two main variables:
The number of triangles ABOVE and BELOW the line
The number of triangles BLACK and WHITE
For the following equations, we subtract the LARGER figure by the ...
It is Sunday.as Day after tomorrow is Tuesday and Tuesday becomes yesterday on Wednesday, so Wednesday is 2 days away( Go backwards, so we have only Monday and Tuesday in between Wednesday and Sunday). Then as day before yesterday would be Friday and Friday would be tomorrow on Thursday. So again Thursday is 2 days away ( Go forward, so we have only Friday ...