Solve Dot Product Riddle in 3 or 1 Guess

In summary, the puzzle involves person A picking three numbers from 0-99 and person B guessing those numbers. Person A then gives the dot product of his chosen numbers with person B's guesses. The challenge is for person B to figure out person A's selected numbers in three guesses, and even more challenging is to do it in one guess. The solution to the first part involves using vectors to represent the guesses, while the second part involves finding a way to formulate the initial guess so that the second guess will always be correct. This can be achieved by having the guesses not restricted to the range of 0-99.
  • #1
Von Neumann
101
4
I was recently posed a riddle that went like the following:

There are two people. Person A picks three numbers from 0-99. Person B guesses which three numbers that person A has picked. Then, person A gives the dot product of his picked numbers with person B's guessed numbers. The question is how could person B figure out person A's selected numbers in three guesses. Even more challenging is to provide a solution that allows person B to guess the numbers in one guess.

I have a solution to the first part:

Think of person A and person B as having their guess put into vectors [itex]\vec{a}[/itex]=(a[itex]_{1}[/itex], a[itex]_{2}[/itex], a[itex]_{3}[/itex]) and [itex]\vec{b}[/itex]=(b[itex]_{1}[/itex], b[itex]_{2}[/itex], b[itex]_{3}[/itex]) respectively. To get the corresponding component a[itex]_{1}[/itex], person B should select the components (1,0,0) so the dot product will yield a[itex]_{1}[/itex]. Same for a[itex]_{2}[/itex] and a[itex]_{3}[/itex]. Simple enough.

The next part I am stumped. The only clue I was given is that person B's three guesses are not restricted between 0-99. Anyone have any insight?
 
Mathematics news on Phys.org
  • #2
The key is that the numbers have a finite length, and can be separated far enough from each other by multiplication for further examination.
 
  • #3
Hey guys!

I had no idea it was so simple! I was looking into it too much. Thanks for the help.
 
  • #4
This also depends upon the value incorporated --In case one is choosing (7 ,77 ,93) as the three value -it may lead to come with 3 guesses .
Finite length numbers can be taken as simple guesses.Comes handy only with vectors
 
  • #5
I'm probably way off here but don't you get a single equation with 3 unknowns? (and a restricted domain)
 
  • #6
Von Neumann said:
Even more challenging is to provide a solution that allows person B to guess the numbers in one guess.
That's one additional guess, not one guess. The conversation would go like this:

Person A: I've picked three numbers from 0-99. Can you guess what they are, in the order in which I picked them? As a hint, I'll tell you the inner product of my numbers and your guess if your guess is wrong.
Person B: OK. Here's my first guess: b1, b2, and b3.
Person A: Hey! That's cheating! It's also wrong. But since I didn't make my rules clear enough, I guess I'll have to tell you that the inner product is c.
Person B: OK! Here's my second guess: a1, a2, and a3.
Person A: Correct.

Two guesses, not one. The puzzle is how to frame the first guess so that the second guess will inevitably be correct.
autodidude said:
I'm probably way off here but don't you get a single equation with 3 unknowns? (and a restricted domain)
No. There is a way (there are an infinite number of ways) to formulate the initial guess so that the second guess will always be correct.
 
  • #7
D H said:
No. There is a way (there are an infinite number of ways) to formulate the initial guess so that the second guess will always be correct.

How? :confused:
 
  • #8
autodidude said:
How? :confused:

Read Ferramentarius' clue again, and note that the guesses for B are not restricted to the range 0-99.
 

1. What is a dot product riddle?

A dot product riddle is a mathematical puzzle that involves finding the dot product of two vectors. The dot product is a mathematical operation that measures the similarity between two vectors and is often used in physics and engineering.

2. How do you solve a dot product riddle in 3 or 1 guess?

To solve a dot product riddle in 3 or 1 guess, you need to use a specific formula to calculate the dot product of the given vectors. This formula involves multiplying the corresponding components of the two vectors and then adding them together. Once you have the dot product, you can use it to determine the answer to the riddle.

3. Can a dot product riddle be solved in more than 3 or 1 guesses?

Yes, it is possible to solve a dot product riddle in more than 3 or 1 guesses. However, using the formula to calculate the dot product allows you to solve the riddle in the fewest number of guesses possible.

4. Why is the dot product important in solving riddles?

The dot product is important in solving riddles because it allows us to measure the similarity between two vectors. In riddles, it is often used to compare different elements or attributes and find patterns or relationships between them.

5. Are there any tips for solving dot product riddles?

Yes, some tips for solving dot product riddles include understanding the concept of dot product, practicing using the formula to calculate it, breaking down the riddle into smaller parts, and looking for patterns or relationships between the given elements. Additionally, having a good understanding of vectors and their properties can also be helpful in solving these riddles.

Similar threads

  • General Math
Replies
4
Views
3K
Replies
9
Views
1K
Replies
8
Views
1K
  • Advanced Physics Homework Help
Replies
3
Views
287
  • Linear and Abstract Algebra
Replies
14
Views
497
Replies
2
Views
2K
Replies
14
Views
1K
  • General Math
Replies
2
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
15
Views
1K
Replies
1
Views
1K
Back
Top