35

Final solution 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 ...


34

The first step is this: Then,


30

There is a trick to this. With that interpretation, the solution is easy. Without this trick


21

Frogs So So So Note that So:


18

Solution 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 ...


18

It's because


15

The frogs really have: Explanation:


13

You can get at most This is possible to achieve: So now we've reduced the problem to the variant where Here's an optimal strategy: This is optimal because:


12

I am able to find a unique answer only if I interpret With that interpretation, my answer is that the friend is pointing to Explanation:


11

By choosing appropriate numbers to write at the start, you can manage it with Here's how. 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 ...


9

I put it into a neater format: Left column: Bottom row: Bottom-right square: Long diagonal: Middle bottom box: Now putting $4$ in B3 leads to So $4$ is in C3. Now putting $3$ in B3 leads to So $2$ is in B3 and $3$ is in C2. Now: So $8$ is in F3. If $4$ is in G1, then Consider the left middle square. Now Long diagonal: Final solution


8

The numbers are: Step 1: Step 2 Step 3 Step 4 Step 5


8

She was The decorator put


8

I think the solution is:


7

They could ... Now So


7

My color scheme is: yellow for "empty", dark gray for "human", red for "vampire", light red for "no human, maybe vampire", and light gray for "no vampire, maybe human". Start with the basic deductions on the 0s: Next, A similar strategy can be used We can also attack the top left in a similar way. And another pair can be attacked: Some miscellaneous ...


7

The same 56 solutions but with logical reasoning instead of bruteforcing:


6

Final solution 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 ...


6

The answer is Logic:


6

The answer maybe: The reason is:


6



5

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


5

First fill in the obvious ones Continue as follows Continue Continue by identifying where bulbs can't be Continue And Finally


5

Here is the solution:


5

There are 56 solutions: I wrote an algorithm to find these solutions.


4

I can prove that is minimal. 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 ...


4

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 ...


4

Final solution 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 ...


4

Without restriction of only checking consecutive papers The general solution for $n$ would be: Visualization: With condition of only checking consecutive papers I believe this is the general equation for $n$: For $n > 2$:


4

Final solution Step-by-step solution 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 ...


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