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6 sawal 6 challenges

July 31, 2013 by puzzler 62 Comments

Collection of these 6 very interesting riddles

  1. Who’s birthday does not came every year?
  2. What does not get dry in sunlight, it even grows?
  3. Which fruit is sweet but still not available for sale in market?
  4. What brakes as soon as you name it?
  5. What is that which runs without legs and never returns back?
  6. Which fish can not swim in sea?

[Read more…]

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River crossing: she-goat, wolf and cabbage

June 13, 2013 by puzzler 6 Comments

A farmer is returning from market, where he bought a she-goat, a wolf and cabbage. On the way home he must cross a river. His boat is little, allowing him to take only one of the three things. He can’t keep the she-goat and the cabbage together (because the she-goat would eat it), nor the she-goat with the wolf (because the she-goat would be eaten). How shall the farmer get everything on the other side (without any harm)?

[Read more…]

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Why manholes are round?

June 10, 2013 by puzzler 6 Comments

Why manhole covers are round in shape then square and any other shape?

Round shape manhole cover

Round shape manhole cover

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3 doors, 2 goats and a car

May 23, 2013 by puzzler 2 Comments

 

3 doors 2 goats and a car problem

3 doors 2 goats and a car problem

Problem Statement

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1.

Now the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to switch and pick door No. 2?”

What should you do? Would you will with your current choice (door no. 1) or should you pick the door no. 2 ?
See AnswerHide Answer

You first though will be to stay, as it has worked out pretty well so far and since there are only two doors, there are fifty-fifty chances of winning the car.
But
Its not right, The best strategy to wins the car is to switch every time as from the below image, if you stay you win one in three times if you switch you win two in three times.

3 doors 2 goats and a car solution

3 doors 2 goats and a car solution

You might still be thinking that there are fifty-fifty chances of winning the game, that is right only when host did not know what was behind the 3rd door, as he knew it already your probability of winning the car will be more when you switch.

Reference: http://www.businessinsider.com/the-most-controversial-math-problems-2013-3#-2

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Number Puzzle #48

May 20, 2013 by puzzler 2 Comments

What is the missing letter?

6 4 4 N 4 1 L 7 5 U 6 10 ? 1 14 2

6 4 4 N
4 1 L 7
5 U 6 10
? 1 14 2

Check your answer:-

Tried enough already?
See ExplanationHide Explanation
Answer is Q
How?
The letter in the box is the nth alphabet where n is the sum of other three numbers.

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Minimum wins to qualify for playoffs

May 6, 2013 by puzzler 1 Comment

 

minimum wins to qualify for playoffs

minimum wins to qualify for playoffs

There are 9 team participating in Indian Premier League, every team will play two matches with every other team. Top 4 teams will be qualified for playoffs.

How many minimum wins required for a team to ensure a place in playoffs?

See SolutionHide Solution
Total number of matches to be played = 9C2 *2 = 9!/(2!7!)*2 = 8*9= 72 and each team will play 16 matches.

Case 1: Lets say if Team A and B and C wins 14 matches each(they will loose 1 game each from other two teams), then team D can win only 16 – 3*2 = 10 matches.

Case 2: Lets take a case where Top 4 team wins 13 games each

Team A: wins 13 matches, looses 3 games from B,C and D
Team B: wins 13 matches, looses 3 games from A,C and D
Team C: wins 13 matches, looses 3 games from A,B and D
Team D wins 13 matches, looses 3 games from A, B and C

Now Team E, can only win maximum of 8 matches as it A,B,C and D will win all matches played by E.

Case 3: Lets say top 5 teams wins 12 matches each

Team A: wins 12 matches, looses 3 games from B, C, D and E
Team B: wins 12 matches, looses 3 games from A, C, D and E
Team C: wins 12 matches, looses 3 games from A, B, D and E
Team D wins 12 matches, looses 3 games from A, B , C and E
Team E wins 12 matches, looses 4 games from A, B, C and D

In this case, team E though wins 12 matches but still don’t qualify for playoffs(assuming lowest run rate).
Thus from case 2 we can say that a team has to win at least 13 matches to ensure a place in playoffs.

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Boy with Toffee #42

April 30, 2013 by puzzler 2 Comments

Boy with Toffees

A boy has few toffees with him, then comes one of his friend and they decide to share them equally and they are able to divide them without any toffee remaining. Then one more friend comes and they divide the toffees in 3 equal parts, then one more friend comes, they are still able to divide the toffees in 4 equal parts, then comes one more friend, they are still able to divide them equally, similarly they are able to divide it equally in 5 and 6 equal parts but not when they are 7 and decide to divide equally they are left with one extra toffee.
Can you tell the minimum number of toffees boy had initially ?

Tried enough already?
See SolutionHide Solution
Since, They are able to divide the toffees equally between 2,3,4,5 and 6 boys so the number of toffees must be a multiple of all of these.
To get the minimum number we should first get the Least Common Multiple of 2,3,4,5 and 5, i.e. 2^2.3^1.5^1 = 60.
Now lets divide it by 7, the remainder is = 4, so it cant be the answer, So we should try the next possible answer i.e. 120, divide it by 7, remainder = 1, so minimum number of toffees boy can have is 120.

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9 digit number #46

April 27, 2013 by puzzler Leave a Comment

9 digit number puzzle

There is a 9 digit number. No digit are repeated and rightmost digit is divisible by 1 and right 2 digits is divisible by 2, right 3 digits is divisible by 3 and so on, finally the whole number is divisible by 9.

Can you find out the number?

See SolutionHide Solution
As the right two digits are divisible by 2, so rightmost digit should be even, at the same time right 5 digits are divisible by 5 so the rightmost digit can be 5 or 0, but as it should be even so it can only be 0.

Now, Right 4 digits are divisible by 4, so the rightmost two digits can be either 20, 40, 80 or 60.
To be divisible by 9 the digits of a number must sum to a multiple of 9. Adding the 10 digits together (0+1+2+…+8+9) gives 45 which is div by 9. However, this is a 9-digit number so we have to drop one from the ten. We can only take out 0 or 9 and still have the remaining digits sum to a multiple of 9. We’ve already shown that 0 is present so the 9 is dropped.
Right 3 digits are divisible by 3 so these 3 digits can be 120, 420, 720, 240, 540, 840, 180, 480, 780, 360.
Now to be divisible by 6 sum of the six digits should be divisible by 3 and it should also be even, which it is.

There is no rule for divisible by 7 so we just have to take digits such that they are divisible by 7, there can be many such numbers and one such number is 123567480.

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Coins and sandwiches

April 23, 2013 by puzzler 1 Comment

Three friends A, B and C went on a trip.
A didn’t carry any food with him but had 13 Coins. B had 6 sandwiches, and C had 7 sandwiches with him (Total 13 Sandwiches).

They decided to share the food equally and in return A would give away all 13 coins to B & C.

How should B & C distribute the money?


Click here to See SolutionHide

Coins and sandwiches solution

Since they have to share the sandwiches equally, each of them will get 13/3 sandwiches.

Hence the sandwiched contributed by B and C to A.
B: 6 – 13/3 = 5/3
C:7 -13/3 = 8/3

Now A should give the money in the ratio of what he got from B and C, i.e.
5/3:8/3 :: 5:8

Hence B will get 5 and C will get 8 coins.

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Number Puzzle #40

April 22, 2013 by puzzler Leave a Comment

 

3,7,5=>26 3,2,1=>5 2,8,6=>44 5,4,9=>?

3,7,5=>26
3,2,1=>5
2,8,6=>44
5,4,9=>?

Check your answer:-

Tried enough already?
See ExplanationHide Explanation
Multiplication of bigger numbers – (square of remaining number).

Checkout more Number Puzzles Tags: medium, Puzzle, Solved Puzzles

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