(Puzzles) Challenging Mathematical Puzzles (33)

Puzzles : Challenging Mathematical Puzzles

111. Substituting these values in equation I, we get
( 4 * Y ) / X = X / Y
4 * Y * Y = X * X
2 * Y = X

Hence, the speed of Bangalore-Mysore train is TWICE the speed of Mysore-Bangalore train.How much faster is one train from other?

Answer :-
49 times

Let's assume that everyone clinked their mug with friend to his left only. It means that there are total 49 clinks. Now the right clink of each person is left clink of the person on right which is already happened. Hence, there are only 49 clinks.

 

112. Karan bought a little box of midget matches, each one inch in length. He found that he could arrange them all in the form of a triangle whose area was just as many square inches as there were matches.

He then used up six of the matches, and found that with the remainder he could again construct another triangle whose area was just as many square inches as there were matches.

And using another six matches he could again do precisely the same.
How many matches were there in the box originally?
Note that the match-box can hold maximum of 50 matches.

Answer : -
Initially, there were 42 or 36 matches in the match-box.

There are 42 matches in the box with which he could form a triangle 20, 15, 7, with an area of 42 square inches. After 6 matches had been used, the remaining 36 matches would form a triangle 17, 10, 9, with an area of 36 square inches. After using another 6 matches, the remaining 30 matches would form a triangle 13, 12, 5, with an area of 30 square inches. After using another 6, the 24 remaining would form a triangle 10, 8, 6, with an area of 24 square inches.

Thus, there are two possible answers. There were either 42 or 36 matches in the match-box. 

 

113. Find the values of each of the alphabets.
N O O N
S O O N
+ M O O N
----------
J U N E

Answer :-
Using trial and error. There are 2 solutions to it and may be more.

2 4 4 2
1 4 4 2
+ 5 4 4 2
----------
9 3 2 6
4 1 1 4
5 1 1 4
+ 0 1 1 4
----------
9 3 4 2

We have to fill number from 1 to 12 at the intersection point of two or more lines. We have to construct a star using two triangle. The sum of all number lying in straight lines should be same. This can be easily understood by the fig. and hence solved.

We have one answer where sum of all the numbers lying in straight lines is 26. 

 

114. Montu, Bantu, Chantu and Pintu have pets.
Montu says, "If Pintu and I each have a dog, then exactly one of Bantu and Chantu has a dog."
Bantu says, "If Chantu and I each have a cat, then exactly one of Montu and Pintu has a dog."
Chantu says, "If Montu and I each have a dog, then exactly one of Bantu and Pintu has a cat."
Pintu says, "If Bantu and I each have a cat, then exactly one of Bantu and I has a dog."
Only one of the four is telling the truth. Who is telling the truth?

Answer : - Bantu is telling the truth.

For a IF-THEN statement to be false, IF part has to be true and THEN part has to be false.


Since only one statement is true and remaining three are false, IF part of three statements are true & THEN part of one statement is true. Let's put the given information in table. The pet-name in the normal text represents the IF part and the pet-name in round brackets represents the THEN part.

 

Montu

Bantu

Chantu

Pintu

Montu says

Dog

(Dog)

(Dog)

Dog

Bantu says

(Dog)

Cat

Cat

(Dog)

Chantu says

Dog

(Cat)

Dog

(Cat)

Pintu says

 

Cat
(Dog)

 

Cat
(Dog)

It is clear that the IF part of the statements made by Montu, Chantu and Pintu are true as they do not contradict each other. And the IF part of the statement made by Bantu is false.

Thus, Bantu is telling the truth.

Montu have a Dog and may or may not have a Cat.
Bantu have a Cat.
Chantu have a Dog.
Pintu have a Dog and a Cat.

 

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