From 0a56bbc480ce8b7e2c80ca6ceb2b0563704002f2 Mon Sep 17 00:00:00 2001 From: matingnet Date: Thu, 26 Dec 2024 15:23:48 +0100 Subject: [PATCH] Add solution Signed-off-by: matingnet --- solutions/my_solution.txt | 87 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 87 insertions(+) create mode 100644 solutions/my_solution.txt diff --git a/solutions/my_solution.txt b/solutions/my_solution.txt new file mode 100644 index 0000000..88d6a05 --- /dev/null +++ b/solutions/my_solution.txt @@ -0,0 +1,87 @@ + + +Steps for Solving the Thirsty Men Problem: + +1. Shuffling the Cups: + - The guests will rearrange their cups such that no one holds their own cup. + - To achieve this, they can stand in a circle and pass their cup to the person on their right. + - This ensures that each guest ends up holding a cup that doesn't belong to them. + +2. Secure Placement Using Encryption: + - Each guest, say Guest X, will create a secret key that is known only to them and the pourer. + - Guest X will then: + - Ask the owner of the cup they are holding to choose a large random number. + - Encrypt this number using their secret key. + - Perform a modulus operation (`mod N`) on the encrypted result to ensure the number falls within the range of available positions (0 to N-1). + - Place the cup they are holding in the position corresponding to the result of the modulus operation. + +3. Validation by the Pourer: + - The pourer, who knows Guest X's secret key, can independently verify that the calculation was done correctly. + - This ensures that Guest X didn’t intentionally place the cup in an incorrect position. + +4. Repeat for All Guests: + - This process is repeated for every guest until all cups are placed in the positions determined by the secure computation. + +-------------------------- + +The following question may arise: +Why is it necessary to shuffle the cups in the first place? + +Answer: +Shuffling the cups ensures fairness and enforces cooperation. Here's why: + +1. Incentive to Follow the Rules: + - When the cups are shuffled, no guest holds their own cup. + - If a guest disobeys the rules, the guest holding their cup will retaliate by refusing to place it on the table. + - As a result, the disobedient guest will have no chance to drink, creating a strong incentive for everyone to follow the rules. + +2. Fair Distribution of Responsibilities: + - Without shuffling, some players (e.g., those assigned the middle positions) might refuse to place their own cups because they perceive it as a disadvantage. + - In the shuffled setup, it is not the cup owner but the person holding the cup who is responsible for placing it, ensuring a fair distribution of responsibilities. + +-------------------------- + +Simulation of the process with three players + +Players and Initial Setup: +1. Players: + - Player A, Player B, Player C. + +2. Cups: + - Each player initially holds their own cup: + - Player A holds Cup A. + - Player B holds Cup B. + - Player C holds Cup C. + +3. Shuffling: + The cups are shuffled so no player holds their own cup: + - Player A holds Cup B. + - Player B holds Cup C. + - Player C holds Cup A. + +Simulation Steps: + +Step 1: Player A’s Turn +- Player A creates a secret key. +- Player A asks the owner of Cup B (Player B) to choose a random number (e.g., 15). +- Player A encrypts the number and calculates the position by performing modulus 3 on the result. +- Result: Player A places Cup B in Position 2. + +Step 2: Player B’s Turn +- Player B creates a secret key. +- Player B asks the owner of Cup C (Player C) to choose a random number (e.g., 9). +- Player B encrypts the number and calculates the position by performing modulus 3 on the result. +- Result: Player B places Cup C in Position 0. + +Step 3: Player C’s Turn +- At this point, only Position 1 is left. +- Player C places Cup A directly in the remaining position (Position 1). + +Final Outcome: +The cups are placed as follows: +- Position 0: Cup C +- Position 1: Cup A +- Position 2: Cup B + +This ensures fairness and adherence to the rules. Each player cooperates because no one holds their own cup, and disobedience results in not being able to drink. +