**if following relationship holds then what is value of 9
4=61
5=52
6=63
7=94
8=46
9=?**

## Confusing one!

a) Q3

b) Q4

c) Q1

d) Q2

a) Q4

b) Q2

c) Q3

d) Q1

Q3. Which is the first question where d) is the correct answer

a) Q1

b) Q2

c) Q4

d) Q3

Q4. Which is the first question where b) is the correct answer

a) Q2

b) Q4

c) Q3

d) Q1

Answers:

d

c

a

b

🙂

## River crossing – the harder one

Now the difficulties are : if the dog is left with anyone and the maid isn’t there to control him, he’ll bite. The dad can’t be left with any of the daughters when the mom isn’t there. Likewise, the mom can’t be trusted alone with either of the sons when the dad isn’t there.

Remember! only an adult can operate the boat, and the boat can’t drive itself.See Solution : River crossing - the harder one

Say

West shore is {W} and East shore is {E}

Lets give the nick names to each family member and dog 😉

Mother – {m}, Father – {F}, Daughters – {d1, d2}, Sons – {s1, s2}

House maid – {h}, Dog – {d}

Initially,

W = {m, d1, d2, f, s1, s2, h, d}

E = {…}

let’s move everyone, over…

housemaid and dog go east, and the housemaid comes back:

W = {m, d1, d2, f, s1, s2, h}

E = {d}

housemaid and s1 go east, h and d come back:

W = {m, d1, d2, f, s2, h, d}

E = {s1}

father and s2 go east, father comes back:

W = {m, d1, d2, f, h, d}

E = {s1, s2}

mother and father go east, mother comes back:

W = {m, d1, d2, h, d}

E = {f, s1, s2}

h and d go east, father comes back:

W = {m, d1, d2, f}

E = {s1, s2, h, d}

father and mother go east, mother comes back:

W = {m, d1, d2}

E = {f, s1, s2, h, d}

mother and d1 go east, housemaid and d come back:

W = {d2, h, d}

E = {m, d1, f, s1, s2}

h and d2 go east, h comes back

W = {h, d}

E = {m, d1, d2, f, s1, s2}

h and d go east

W = {}

E = {m, d1, d2, f, s1, s2, h, d}

And we are done.

## Defective coins

We have 10 bags of 1 Rupee coins. One bag contains all the defective coins, the weight of each coin in that bag is 1 gram lesser than the weight of a normal 1 Rupee coin. You have a spring balance, which tells the exact weight. After how many minimum no. of weighs you can separate the bag with defective coins.

**Other variant of the same problem:**

There are 10 machines in a factory. Each produces coins weighing 10 grams each. One day the factory owner cones to know that one of the machine is not functioning properly and produces coins of weight 9 grams. You have to find out the faulted machine. You ONLY have a weighing machine and you can use it only ONCE.

Want to try now ?

solution :

Let P is the no. of the bag which contains the defective coins.

Then S = (W grams)*(1+2+3….+10) – P*(1 gram)

P will come out to be a number between 1 to 10 and thats the required bag.

## Hats and IIT students

Prof goes out and comes back after 20 minutes but nobody was able to answer the question. So he gave them 10 more minuets but the result was the same. So he decides to give them final 5 minutes. When he comes everybody was able to answer him correctly.

So what is the answer? and why?

See Solution : Hats and IIT studentsAfter first interval of 20 minutes :

So there can not be 1 red and 8 black hats.

After second interval of 10 minutes :

So there can not be 2 red and 7 black hats.

After third interval of final 5 minutes :

So there are 3 red hats and 6 black hats.

## River crossing

Note that if a boat with a cannibal and an anthropologist travels to a shore with one cannibal on it, then no. of cannibals > no. of anthropologists, even if you say the anthropologist immediately takes the boat back.See Solution : River crossing

Let

C = Cannibal

B = the boat

W = the west shore (which they are all on)

and E = the east shore (where they want to go)Step 1 : A and C crosses

W [A, A, C, C] E [A, C, B]Step 2 : A returns

W [A, A, A, C, C, B] E [C]Step 3 : Two C crosses

W [A, A, A] E [C, C, C, B]Step 4 : C returns

W [A, A, A, C, B] E [C, C]Step 5 : Two A crosses

W [A, C] E [A, A, C, C, B]Step 6 : A and C returns

W [A, A, C, C, B] E [A, C]Step 7 : Two A crosses

W [C, C] E [A, A, A, C, B]Step 8 : C returns

W [C, C, C, B] E [A, A, A]Step 9 : Two C crosses

W [C] E [A, A, A, C, C, B]Step 10 : C returns

W [C, C, B] E [A, A, A, C]

Step 11 : Two C crosses

W [Empty]
E [A, A, A, C, C, C, B]

## Average salary

Three coworkers would like to know their average salary. How can they do it, without disclosing their own salaries to other two?

See Solution : Average salaryLet the three persons are A, B and C. Now first A tells the sum of his salary and a random number to B , lets say (SA + A(random no. of A)). Now B adds the sum of his salary and a random number to the number given by A i. e. B makes the total = (SA +A) + (SB+B) and he passes this number to C. (at each step, they don’t show the no. to the third person). Now C does the same, adds his salary and a random number to the amount told by B. Now C passes this total equals to (SA+SB+SC+A+ B+C) to A. Now A subtracts his random no. (A), passes to B then B subtracts his random no. (B) and passes to C. Finally C subtracts his random no. (C) and tells everybody. They divide it by 3. Now they have the average salary.

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