70
Yes.
Guess 1st set (1,3,5,7,9,11,13,15) -> If the number is in the set, write down 1
Guess 2nd set (2,3,6,7,10,11,14,15) -> If the number is in the set, write down 2
Guess 3rd set (4,5,6,7,12,13,14,15) -> If the number is in the set, write down 4
Guess 4th set (8,9,10,11,12,13,14,15) -> If the number is in the set, write down 8
After all 4 guesses, add the ...
54
A simple way is to pick the number $X$ which is half-way through the range and ask
Is it less than $X$?
From the answer you can discard either the lower half or the upper half of the range.
Repeat until you have 1 number left.
This method is known as a binary search or binary chop.
In general, If you are allowed $q$ queries, you can get an answer from ...
42
The result of 7@6 is
because
23
To build off @ChrisCudmore’s correct answer (go upvote it!), here is the same answer but with a simpler less technical explanation – hopefully this will be easier to understand…
If you are allowed to ask four questions before then saying which number it is, you should use the following 4 questions:
Now to find the number, start with 0.
You will always get ...
13
The answer is
because the operator x@y is clearly the function:
Alternatively:
11
You can do this by splitting the range in half. If the numbers to guess from (1-16) is less than 2^X where x is the number of guesses you get. Look at the picture below, and each color is 1 guess:
Hypothetically, the answer is 16 (I rounded up to split the numbers easier).
1. you guess 1-8, and that isn't it
2. you guess 9-12 and that isn't it
3. you guess ...
8
The maximum is
Reasoning
7
The answer may be
because
fits for the given examples.
5
Since we are talking about multiplication (products grow really fast), and our data gathering is relatively cheap, it stands to reason that the best strategy is to
I had this idea yesterday, but it took me this long to get through the final annoying special case. However, I'm pretty convinced now that
This is going to be a longish read because of the ...
5
Maybe would be worth a try to go for:
5
Slightly simplifying Dark Malthorp's remarkable solution, we get: $$\pi \approx A_k = \left[1 - \left( 2 \cdot \log\lceil \sqrt{3!_k}\rceil + \sqrt{4}\right)\div(\lfloor\sqrt{\lceil\sqrt 5\rceil!_k}\rfloor!)\right]^{\lceil\sqrt{6!_{k-1}}\rceil!} \div \lfloor\sqrt 7\rfloor \cdot \lceil\sqrt{\lceil\sqrt 8\rceil!_k} \rceil!\cdot \lfloor\sqrt{\sqrt{9}!_k}\rfloor!...
4
Expanding on @Dason's answer:
2
No, it is not possible.
At least not unless you put up more restrictions. E.g. that the numbers have to be integers.
None of the solutions shown so far give a way to find $\sqrt \pi$ , which is between 1-15.
If you restrict yourself to integers you can use this method:
sum = 0
s = 1
while s <= max value:
Ask: "Is the number odd?"
Yes: Add s to sum
...
2
Maybe her 4-digit password is:
Reason:
2
So I can’t comment since I don’t have enough reputation yet. I just want to say that this is the coolest thing I have ever seen. I had no idea that binary could be used in such a way that you could guess a number in a certain amount of guesses 100% of the time as long as the amount of guesses was equal to the amount of digits in binary of the highest number ...
1
1
There are 2 problems with trying to eliminate half of the numbers between 1-15
1st problem: you eventually narrow it down to 2 numbers at which point you have to ask about 1 specific number which isn’t allowed.
2nd problem: if the questions aren’t answered when they’re asked, but rather all 4 questions are answered after they’re all asked, then ...
1
1
I think it's unlikely that this is really the solution, since you could make up several similar ways of "solving" the puzzle, but maybe it's worth a try.
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