Plan The Best Chance of Winning!

You are playing a game of dodge ball with two other people, John and Tom. You're standing in a triangle and you all take turns throwing at one of the others of your choosing until there is only one person remaining. You have a 30 percent chance of hitting someone you aim at, John has a 50 percent chance, and Tom a 100 percent change (he never misses). If you hit somebody they are out and no longer get a turn.

If the order of throwing is you, John, then Tom; what should you do to have the best chance of winning?

This should be you plan to increase chances of winning! 

Planning The Best Chance of Winning!

What was the game?

You should miss the first shot for the purpose.

Remember, about one of your 3 shots (30% accuracy), John's 1 out of 2 shots (50% accuracy) and Tom's every shot is on target.

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CASE 1 : If you target Tom and hit him then John has to hit you. Even if he fails to target you in first attempt he will be successful in his second attempt. 

And since, your first shot was on target your next 2 has to be off the target one of which will give John a second chance.


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CASE 2 : If you target John then Tom will certainly hit you to be winner of the game.

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CASE 3 : Better miss the first shot and then 1 of next 2 shots will be on the target.

Now, John has to target Tom otherwise assuming John as stronger player, Tom will eliminate him immediately. 

    CASE 3.1 : If John hits Tom and eliminates him then it's your turn

                     now and John's next attempt has to be off the target. 

                     So, even if you fail in first try after John's

                      unsuccessful try you can surely hit John in second try.

    CASE 3.2 : And if John misses Tom then Tom will throw John 

                     out of game in his first attempt. Now, it's your turn 

                     and you can target Tom with 50% accuracy.

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This is the best plan to get a chance of winning this game. 

Angles on Christmas Tree in Puzzle!

Four angels sat on the Christmas tree amidst other ornaments. Two had blue halos and two - yellow. However, none of them could see above his head.

Angel A sat on the top branch and could see the angels B and C, who sat below him. Angel B, could see angel C who sat on the lower branch. And angel D stood at the base of the tree obscured from view by a thicket of branches, so no one could see him and he could not see anyone either.

Which one of them could be the first to guess the color of his halo and speak it out loud for all other angels to hear?

THESE angels have maximum chance of correct guess!


Similar Puzzle 

Logical Angels on Christmas Tree

How their logical skills are challenged?

Case 1 :

The angel A observes that the aureoles of B and C are of the same color. Then, A can be sure that the color of own aureoles must be other than that of B and C.

So, A will be the first to guess the correct color in case he observes 2 same colored aureoles B and C.

Case 2 :

The angle D notices that the color of aureoles of B and C are different. Now, A has to remain silent. The silence of A suggests B that the color of aureole of B must be different than the C.

So, in that case, B will be the first one to guess correct color of own aureole.

However, C has no chance to guess the color of own aureole unless, A or B reveals color of own aureole. And D has absolutely no chance of correct guessing the color of own aureole.

Will the Sheep Survive?

Hundred tigers and one sheep are put on a magic island that only has grass. Tigers can live on grass, but they want to eat sheep. If a Tiger bites the Sheep then it will become a sheep itself. If 2 tigers attack a sheep, only the first tiger to bite converts into a sheep. Tigers don’t mind being a sheep, but they have a risk of getting eaten by another tiger.

All tigers are intelligent and want to survive. 

Will the sheep survive?

Survival chances of the sheep are - Click Here! 

Survival Chances of the Sheep

Why sheep is in danger?

First let's see what happens when there are different number of tigers present on 
the island. Remember we are talking about survival of the sheep that is initially present n the island and not sheep converted from tiger.

1. Suppose there are only 1 tiger and 1 sheep on the island. Then, the tiger will eat 
    the sheep and won't have fear of being eaten up after transformation into sheep 
    as there is not tiger left. 

    The sheep will not survive.

2. Let's suppose there are 2 tigers and 1 sheep present. Each intelligent tiger can think - 

    ----------------------------------------------------------------------------------------------------------
   "If I eat a sheep then I will be converted into sheep and other tiger would eat me
    as it would result into '1 tiger and 1 sheep' scenario above in (1). 

    So, I should not take risk"
    ---------------------------------------------------------------------------------------------------------- 

    The sheep will be survived.


3. Now suppose there are 3 tigers and 1 sheep are on the island. Each tiger would think-  
     ----------------------------------------------------------------------------------------------------------
    "If I target the sheep and get converted into sheep itself then on the island there
     would be 2 tigers and 1 sheep as above case (2). 

     As per that, none of other 2 tiger would dare to attack me and I would be 
     survived as a sheep in the end. 

     So better I should attack the sheep and anyhow I will be survived in the end as a
     sheep"
     ----------------------------------------------------------------------------------------------------------
      The sheep will not survive.

4. Finally, suppose there are 4 tigers and 1 sheep. Now, each tiger can put logic like -       ----------------------------------------------------------------------------------------------------------
    "If I attack the only sheep and get myself converted to sheep then this case 
     will be reduced to '3 tigers and 1 sheep' as in case (3). 

     In that case, the sheep has 0 chance of survival in the end. 

     That means, my life will be in danger as in above case (3), if I attack 
     this sheep toget converted into sheep. Better, I shouldn't attack"
     ----------------------------------------------------------------------------------------------------------
     The sheep will be survived.

Conclusion : 

If observed carefully, it can be concluded that the sheep will be survived when there are EVEN number of tigers (Case 2 and Case 4) are present. And obviously, will be in danger when there are ODD number of tigers present on the island.

In the given situation, there are 100 tigers on the island which is EVEN number. That means, as per above conclusion the only sheep on the island will be survived.

 

The Last Bean in the Pot

A pot contains 75 white beans and 150 black ones. Next to the pot is a large pile of black beans. 

A somewhat demented cook removes the beans from the pot, one at a time, according to the following strange rule: 

He removes two beans from the pot at random. If at least one of the beans is black, he places it on the bean-pile and drops the other bean, no matter what color, back in the pot. If both beans are white, on the other hand, he discards both of them and removes one black bean from the pile and drops it in the pot.
 
At each turn of this procedure, the pot has one less bean in it. Eventually, just one bean is left in the pot. What color is it?

And the color of last bean is......