The Millennium Great Mind challenge (Puzzle 2)
Points : 20
You and three of your friends formed up a team to participate in Millennium Great Mind challenge. Your team has advanced to the final round.
In the final round, three of you are made to sit in a closed room, the fourth one is allowed to stand outside the room such that he can hear the voice from inside but can not see any of them. You being the smartest of all, are selected to be the fourth player as your role decides the fate of your team.
Now the game goes like this:
Each one of the three players inside the room are made to wear t-shirts with some positive integer written at its back such that the number on one of the t-shirts is equal to the sum of the numbers on the other two t-shirts.
They are made to sit in such a way that every player can see the number on t-shirt of every other player but not of his own. Each player inside the room can either guess the number on his t-shirt and finish the proceedings inside the room or simply say PASS and pass the turn. An incorrect guess will result in a defeat.
Once the proceedings inside the room are over, the one outside is required to guess the other two numbers based on the last announcement. If he does it right, the team wins else it loses.
The Actual Game
Inside the room- Turn #1
- Player 1: Pass
- Player 2: Pass
- Player 3: Pass
- Turn #2
- Player 1: Announces number on his t-shirt as 50
- Proceedings inside the room finish.
Now you (fourth player) are required to guess the numbers on t-shirt of other two players. How will you make your team win the game? Explain your logic.
Solution
Each person knows that the number on his t-shirt is either the sum or the difference of the other two. He also knows his number is positive.
The fact that Player1 can guess correct number on his t-shirt in his first turn is only possible if he sees equal numbers on other two player's t-shirt. Therefore, Player1's pass response in his turn rules out the possibility of numbers on t-shirt in the ratio 2:1:1.
Similarly Player2's pass response in his turn rules out the possibility of the numbers in the ratio as 1:2:1 and 2:3:1 (as 2:1:1 is not possible).
Similarly Player3's pass response in is turn rules out the posiibility of the numbers in the ratio as 1:1:2, 2:1:3, 1:2:3 and 2:3:5.
Now in the second turn Player1 will say no unless the numbers are in the ratio 3:2:1 or 4:3:1 or 3:1:2 or 4:1:3 or 5:2:3 or 8:3:5. But now in the second turn Player1 guesses his number correctly as 50 and for all the numbers to be positive only 5:2:3 satisfies the above condition.
Therefore the numbers on other two players' t-shirts are 20 and 30 respectively.
This Puzzle was based on the famous puzzle Sum of Hat's Puzzle.
Post your queries regarding the solution at Puzzle 2 Forum Thread.
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discussions
| solver | player places |
| Q: | Can players change thier places after game start. |
| A: | No |
| anshu_iiita | can other players answer their number? |
| Q: | instead of player1, can player2 or player3 answer the number on their shirt? |
| A: | The proceedings of the given actual game can not be changed. You are required to explain how player1 could answer the number in his t-shirt and the corresponding numbers on t-shirts of other players. |
| anshu_iiita | Passes |
| Q: | Let there be three numbers player1=1,player2=2 and player3=3.nnIs it necessary that player1 should pass to player2 only or can he pass to player3 also? |
| A: | The order of pass is fixed. Player1 to Player2 to Player 3 to PLayer 1. |
| Multifarious | Guessing other numbers |
| Q: | Do you have the specify which number belongs to which specific player? For instance, if the other numbers are 1356 and 1306, do you have to say Player 3 has 1356 and Player 2 has 1306? Or will just giving the numbers suffice? |
| A: | You have to specify which number belong to which player. |
| mayankg | answering 50 correctly |
| Q: | Are we expected to tell the strategy behind answering 50 correctly. |
| A: | Yes, this is what the last statement of the problem says. |
| ReDucTor | Limit on passed? |
| Q: | Is there a limit on the number of rotations in passing? |
| A: | In the given actual game, there was just one complete pass and in the turn 2, player 1 answered correctly. You do not need to solve the problem for general case but only for the given case. |
| neetu | pass |
| Q: | can player1 pass question to a particular player3 or player 2 as he wish to do OR it is a cyclic process i.e player1 pass to player2 and then to the player3. Is there any certain number of passes that a player can say? |
| A: | Yes it is a cyclic process in the fixed order 1, 2, 3. There could have been any number of passes. But, you are required to figure out the numbers only for the given actual game. |
| harish610 | Does he answered correctly? |
| Q: | Does the procedure ended because he guessed correctly? Is 50 he answered correct or not? |
| A: | Yes, the procedure ended because the first player guessed 50 correctly. |
| codeyou | zero |
| Q: | can any number be zero? |
| A: | No. As clearly mentioned, all numbers are positive integers. |
| anshu_iiita | How the Game ends |
| Q: | when proceeding inside the room will over.As soon as any player speaks a number(like in given example) or they can continue till they want. |
| A: | The given game proceedings is not an example. You have to guess the numbers on the t-shirts of other two players only for this case. |
| anshulguleria90 | other two players |
| Q: | can we ask more questions from the player? or can we communicate with the players i.e. if we want to a question from the player2 then can we? |
| A: | No other query except for the number on the t-shirt is allowed. The three members are not allowed to talk to each other, but they can ofcourse listen to each other's reply |
