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63 Puzzles Questions And Answers

1⟩ A rich man died. In his will, he has divided his gold coins among his 5 sons, 5 daughters and a manager. According to his will First give one coin to manager. 1/5th of the remaining to the elder son. Now give one coin to the manager and 1/5th of the remaining to second son and so on..... After giving coins to 5th son, divided the remaining coins among five daughters equally. All should get full coins. Find the minimum number of coins he has?

We tried to find out some simple mathematical method and finally we wrote small C program to find out the answer. The answer is 3121 coins.

Here is the breakup:

First son = 624 coins

Second son = 499 coins

Third son = 399 coins

Forth son = 319 coins

Fifth son = 255 coins

Daughters = 204 each

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2⟩ If you look at a clock and the time is 315. What is the angle between the hour and the minute hands? ( The answer to this is not zero!)?

7.5 degrees

At 3:15 minute hand will be perfactly horizontal pointing towards 3. Whereas hour hand will be towards 4. Also, hour hand must have covered 1/4 of angle between 3 and 4.

The angle between two adjacent digits is 360/12 = 30 degrees.

Hence 1/4 of it is 7.5 degrees.

in a one minute minute hand travel six degree and in a one minute hour hand travel half degree.in a three o clock there is nienty degree angle so when minute hand travel ninty degree in 15 minute and hour hand also travel 7.5 degree.so there is 7.5 degree angle is formed.

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3⟩ A cricket team of 11 players lined up in a straight line to have their photograph. The captain was asked to stand in the center of the line-up. 1) Bharat and Bhavin stood to the right of the captain 2) Two players stood between Bhagat and Bhairav 3) Seven players stood between Bhadrik and Bhanu 4) Bhavesh stood to the right of Bhuvan 5) Bhola and Bhumit stood either side of Bhagat 6) Bhavik and Bhumit stood to the left of the captain 7) Six players stood between Bhavin and Bhagat 8 ) Two players stood between Bhagat and Bhavik Who is the captain? Can you tell the positions of all the palyers?

Players from left to right : Bhavik, (Bhadrik/Bhanu), (Bhola/Bhumit), Bhagat, (Bhola/Bhumit), BHUVAN, Bhairav, (Bharat/Bhavesh), (Bharat/Bhavesh), (Bhadrik/Bhanu), Bhavin

Let's number the positions 1 to 11 from left to right. Hence, the captain is at position 6. Now, looking at the clues 7, 5, 2 and 8 together:

Poistion 1 - Bhavik or Bhairav

Position 3 - Bhumit or Bhola

Position 4 - Bhagat

Position 5 - Bhumit or Bhola

Poistion 7 - Bhavik or Bhairav

Position 11 - Bhavin

From clue (3), the only possible positions for Bhadrik and Bhanu are Position 2 and Position 10.

Now there are 3 positions remaining - 6, 8 and 9 and remaining 3 players are Bhuvan, Bharat and Bhavesh. But from clue (1), Bharat stood to the right of the captain i.e. Bharat must be on position 8 or 9 as position 6 is for the captain. So either Bhuvan or Bhavesh is the captain.

From (4), Bhavesh stood to the right of Bhuvan. Hence, Bhuvan is the captain.

Players from left to right are : Bhavik, (Bhadrik/Bhanu), (Bhola/Bhumit), Bhagat, (Bhola/Bhumit), BHUVAN, Bhairav, (Bharat/Bhavesh), (Bharat/Bhavesh), (Bhadrik/Bhanu), Bhavin.

Thus,

* Bhavik(1), Bhagat(4), Bhuvan(6), Bhairav(7) and Bhavin(11) are the players whose positions are fixed.

* Bhadrik and Bhanu are at position 2 or 10.

* Bhola and Bhumit are at position 3 or 5.

* Bharat and Bhavesh are at position 8 or 9.

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4⟩ Substitute digits for the letters to make the following relation true. S T I L L + W I T H I N -------------------- L I M I T S Note that the leftmost letter cant be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter S, no other letter can be 3 and all other S in the puzzle must be 3?

The value of L must be one more than W i.e. L=W+1 and there must be one carry from S+I=I. Also, the value of S must be 9 as S+I=I with one carry from T+T=M, which means that the value of T must be greater than 4.

From I+H=I, the value of H must be 0 as the value of S is 9.

Now, applying all those constraints and using trial-n-error, we get two possible answers.

9 7 1 6 6 9 8 5 3 3

+ 5 1 7 0 1 3 + 2 5 8 0 5 6

--------------- ---------------

6 1 4 1 7 9 3 5 6 5 8 9

The second answer

258056

+98533

---------

356589

is wrong as the value of both N and M is 6 here.

I have tried all the combinations and there seems to be only one solution i.e. the first one

517013

+ 97166

----------

614179

The other constraints that i have found while solving the question are :

L cant be 1

N cant be 8

H = 0

T can have only values 6/7/8

and corresponding M is 2/4/6

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5⟩ Consider an n by n grid of squares. A square is said to be a neighbour of another one if it lies directly above/below or to its right/left. Thus, each square has at most four neighbours. Initially, some squares are marked. At successive clock ticks, an unmarked square marks itself if at least two of its neighbours are marked. What is the minimum number of squares we need to mark initially so that all squares eventually get marked?

3 square marks initially at location (1,1), (1,2) and (2,1). Then it marks all square by considering atleast 2 marks square.

For an nxn grid of square, initially n squares should be marked in appropriate places so as to obtain solution....

Appropriate places should be chosen such that 2 initially marked squares should be neighbor of an unmarked square... Other initially marked squares should be placed such that, it should help in marking further squares...

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6⟩ There are 10 statements written on a piece of paper 1. At least one of statements 9 and 10 is true. 2. This either is the first true or the first false statement. 3. There are three consecutive statements, which are false. 4. The difference between the numbers of the last true and the first true statement divides the number, that is to be found. 5. The sum of the numbers of the true statements is the number, that is to be found. 6. This is not the last true statement. 7. The number of each true statement divides the number, that is to be found. 8. The number that is to be found is the percentage of true statements. 9. The number of divisors of the number, that is to be found, (apart from 1 and itself) is greater than the sum of the numbers of the true statements. 10. There are no three consecutive true statements. Find the minimal possible number?

The numebr is 420.

If statement 6 is false, it creates a paradox. Hence, Statement 6 must be true.

Consider Statement 2:

* If it is true, it must be the first true statement. Otherwise, it creates a paradox.

* If it is false, it must be the second false statement. Otherwise, it creates a paradox.

In both the cases, Statement 1 is false.

As Statement 1 is false, Statement 9 and Statement 10 both are false i.e. there are three consecutive true statements.

1 2 3 4 5 6 7 8 9 10

False - - - - True - - False False

Let's assume that Statement 3 is false i.e. there are no three consecutive false statements. It means that Statement 2 and Statement 8 must be true, else there will be three consecutive false statements.

1 2 3 4 5 6 7 8 9 10

False True False - - True - True False False

Also, atleast two of Statements 4, 5 and 7 must be true as there are three consecutive true statements.

According to Statement 8, the number that is to be found is the percentage of true statements. Hence, number is either 50 or 60. Now if Statement 7 is true, then the number of each true statement divides the number, that is to be found. But 7 and 8 do not divide either 50 or 60. Hence, Statement 7 is false which means that Statement 4 and 5 are true. But Statement 5 contradicts the Statement 8. Hence, our assumption that Statement 3 is false is wrong and Statement 3 is true i.e. there are 3 consecutive false statements which means that Statement 8 is false as there is no other possibilities of 3 consecutive false statements.

Also, Statement 7 is true as Statement 6 is not the last true statement.

1 2 3 4 5 6 7 8 9 10

False - True - - True True False False False

According to Statement 7, the number of each true statement divides the number, that is to be found. And according to Statement 5, the sum of the numbers of the true statements is the number, that is to be found. For all possible combinations Statement 5 is false.

There 3 consecutive true statements. Hence, Statement 2 and Statement 4 are true.

1 2 3 4 5 6 7 8 9 10

False True True True False True True False False False

Now, the conditions for the number to be found are:

1. The numebr is divisible by 5 (Statement 4)

2. The numebr is divisible by 2, 3, 4, 6, 7 (Statement 7)

3. The number of divisors of the number, that is to be found, (apart from 1 and itself) is not greater than the sum of the numbers of the true statements. (Statement 9)

The minimum possible number is 420.

The divisors of 420, apart from 1 and itself are 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210. There are total of 22 divisors. Also, the sum of the numbers of the true statements is 22 (2+3+4+6+7=22), which satisfies the third condition.

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7⟩ In the middle of the confounded desert, there is the lost city of "Ash". To reach it, I will have to travel overland by foot from the coast. On a trek like this, each person can only carry enough rations for five days and the farthest we can travel in one day is 30 miles. Also, the city is 120 miles from the starting point. What I am trying to figure out is the fewest number of persons, including myself, that I will need in our Group so that I can reach the city, stay overnight, and then return to the coast without running out of supplies. How many persons (including myself) will I need to accomplish this mission?

Total 4 persons (including you) required.

It is given that each person can only carry enough rations for five days. And there are 4 persons. Hence, total of 20 days rations is available.

1. First Day : 4 days of rations are used up. One person goes back using one day of rations for the return trip. The rations remaining for the further trek is for 15 days.

2. Second Day : The remaining three people use up 3 days of rations. One person goes back using 2 days of rations for the return trip. The rations remaining for the further trek is for 10 days.

3. Third Day : The remaining two people use up 2 days of rations. One person goes back using 3 days of rations for the return trip. The rations remaining for the further trek is for 5 days.

4. Fourth Day : The remaining person uses up one day of rations. He stays overnight. The next day he returns to the coast using 4 days of rations.

Thus, total 4 persons, including you are required.

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10⟩ What are the next three numbers in the given series? 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 ?

The next three numbers in the series are 4, 3, 4.

The pattern is - the number of 1's in the binary expansion of the positive integers starting from 1.

Number Binary Equivalent # of 1's

1 1 1

2 10 1

3 11 2

4 100 1

5 101 2

6 110 2

7 111 3

8 1000 1

9 1001 2

10 1010 2

11 1011 3

12 1100 2

13 1101 3

14 1110 3

15 1111 4

16 10000 1

17 10001 2

18 10010 2

19 10011 3

20 10100 2

21 10101 3

22 10110 3

23 10111 4

24 11000 2

25 11001 3

26 11010 3

27 11011 4

28 11100 3

29 11101 4

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11⟩ Substitute digits for the letters to make the following Division true O U T ------------- S T E M | D E M I S E | D M O C ------------- T U I S S T E M ---------- Z Z Z E Z U M M -------- I S T Note that the leftmost letter cant be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter M, no other letter can be 3 and all other M in the puzzle must be 3?

C=0, U=1, S=2, T=3, O=4, M=5, I=6, Z=7, E=8, D=9

It is obvious that U=1 (as U*STEM=STEM) and C=0 (as I-C=I).

S*O is a single digit and also S*T is a single digit. Hence, their values (O, S, T) must be 2, 3 or 4 (as they can not be 0 or 1 or greater than 4).

Consider, STEM*O=DMOC, where C=0. It means that M must be 5. Now, its simple. O=4, S=2, T=3, E=8, Z=7, I=6 and D=9.

O U T 4 1 3

------------- -------------

S T E M | D E M I S E 2 3 8 5 | 9 8 5 6 2 8

| D M O C | 9 5 4 0

------------- -------------

T U I S 3 1 6 2

S T E M 2 3 8 5

---------- ----------

Z Z Z E 7 7 7 8

Z U M M 7 1 5 5

-------- --------

I S T 6 2 3

Also, when arranged from 0 to 9, it spells CUSTOMIZED.

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12⟩ 500 men are arranged in an array of 10 rows and 50 columns according to their heights. Tallest among each row of all are asked to come out. And the shortest among them is A. Similarly after resuming them to their original positions, the shortest among each column are asked to come out. And the tallest among them is B. Now who is taller A or B ?

No one is taller, both are same as A and B are the same person.

As it is mentioned that 500 men are arranged in an array of 10 rows and 50 columns according to their heights. Let's assume that position numbers represent their heights. Hence, the shortest among the 50, 100, 150, ... 450, 500 is person with height 50 i.e. A. Similarly the tallest among 1, 2, 3, 4, 5, ..... 48, 48, 50 is person with height 50 i.e. B

Now, both A and B are the person with height 50. Hence both are same.

In that question you mention 500 mens know then how will you say a&b both are persons

please clarify my doubt

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17⟩ A man got up at 9 a.m. He became so engrossed in his newspaper he did not have time to go out and shop as he had planned. At 11 a.m. he went for a flying lesson. He carefully followed all the instructions given to him by his instructor until he came in to land. He then ignored his instructor and crashed the plane killing them both. The accident would not have happened if he had gone shopping, which just goes to show how important shopping can be. Why should this be so?

The man had neglected to buy a new battery for his hearing aid. The old battery failed just as he was coming in to land and he therefore did not hear his tutor's crucial instructions.

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