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...... 

The Color of Last Bean in the Pot

Little story behind the title!

There are 75 WHITE beans in the pot i.e. they are odd in numbers. Since, they are always taken out in pair, in the end there will be 1 WHITE bean left out.

At some point, when there are 3 bean are left in the pot then there has to be 2 BLACK and 1 WHITE beans in the pot. They can't be 1 BLACK and 2 WHITE beans as for that 73 WHITE beans need to be taken out which is not possible since WHITE are always taken in pair.

So if cook pick 2 BLACK beans (or BLACK & WHITE) at this point then anyhow BLACK and WHITE will be left in the pot. Now, when he pick this pair of BLACK and WHITE then he puts BLACK on the pile and drop WHITE back to the pot as per his rule.

Eventually, WHITE bean will be left in the pot.

MPSC मध्ये विचारला गेलेला प्रश्न

सोडवा गणित

तुम्ही एका यात्रेत आहत,

त्या यात्रेत तुम्हाला काही प्राणी खरेदी करायचे आहेत.त्या प्राण्यांची किमंत खालील प्रमाणे....

*१० रुपयाला - १ हत्ती

* १ रुपयाला - १ घोडा

* १ रुपयाला - ८ उंट

आणि तुमच्याकडे १०० रुपयेच आहेत.प्राण्याची संख्या १०० च आली पाहिजे.

वरील सगळे प्राणी घेणे बंधनकारक आहे.

कसे येतील.???

प्रश्न कठीण वाटतोय का ? उत्तरासाठी येथे क्लिक / टॅप करा.

👉  वाचा -  गोष्ट विषमासूर नावाच्या राक्षसाची !  

MPSC प्रश्नाचे उत्तर : यात्रेतील प्राणी खरेदी

जाणून घ्या काय होता प्रश्न ?

यात्रेमध्ये कोणता प्राणी किती किंमती मध्ये मिळतो ते पाहुयात.

* १० रुपयाला - १ हत्ती

* १ रुपयाला - १ घोडा

* १ रुपयाला - ८ उंट

म्हणजेच १ उंट १/८ रुपयांना मिळतो.

समजा आपण ' क्ष ' हत्ती, ' य ' घोडे आणि ' ज्ञ ' उंट घेतले तर क्ष हत्तींची किंमत होईल १०क्ष, य घोड्यांची किंमत होईल १य आणि ज्ञ उंट (१/८)ज्ञ रुपयांना पडतील. 

आपल्याजवळ १०० रुपये आहेत म्हणजे - 

१०क्ष + य + (१/८)ज्ञ = १००   ......... (१)

आणि आपल्याला एकूण १०० प्राणी घ्यायचे आहेत म्हणजेच -

क्ष + य + ज्ञ = १००

य = १०० - क्ष - ज्ञ          ....... (२)

समीकरण (२) हे (१) मध्ये टाकल्यानंतर,

१०क्ष + (१०० - क्ष - ज्ञ) + (१/८)ज्ञ = १००

९क्ष + १०० - ज्ञ + (१/८)ज्ञ = १००

९क्ष - (७/८)ज्ञ = ०

९क्ष = (७/८)ज्ञ 

क्ष/ज्ञ = ७/७२. 

याचाच अर्थ क्ष = ७ आणि ज्ञ = ७२ व म्हणूनच य = १०० - क्ष - ज्ञ = १०० - ७ - ७२ = २१ असू शकतो.  

म्हणजेच आपण ७० रुपयांचे ७ हत्ती, २१ रुपयांचे २१ घोडे आणि ९ रुपयांचे ७२ उंट खरेदी करायला हवेत जेणेकरून १०० रुपयांमध्ये १०० प्राण्यांची खरेदी पूर्ण होईल.  

एकूण खर्च = ७० + २१ + ९ = १००. 

एकूण प्राणी = ७ + २१ + ७२ = १००.  

One More Alphamatic Problem?

In the following  puzzles, replace the same characters by the same numerals

so that the mathematical operations are correct.
               

Note - Each letter represents a unique digit and vice-versa.

ABCB - DEFC = GAFB

     :          +      -
  DH  x     AB =    IEI
---------------------------
 GGE + DEBB = DHDG

Here is the SOLUTION