Brain Teaser No : 00007
On one side of a card is written :
"THE SENTENCE ON THE OTHERSIDE OF THIS CARD IS TRUE."
On turning the card over you find:
"THE SENTENCE ON THE OTHERSIDE OF THIS CARD IS FALSE."
Which sentence is true?
Answer
It's a Paradox. Both the sentences are contradictory to each other. If you say that the first sentence is true, then the second will
contradict it and vice versa.
Brain Teaser No : 00008
3 blocks are chosen randomly on a chessboard. What is the probability that they are in the same diagonal?
Answer
There are total of 64 blocks on a chessboard. So 3 blocks can be chosen out of 64 in 64C3 ways.
So the sample space is = 41664
There are 2 diagonal on chessboard each one having 8 blocks. Consider one of them.
3 blocks out of 8 blocks in diagonal can be chosen in 8C3 ways.
But there are 2 such diagonals, hence favourables = 2 * 8C3 = 2 * 56 = 112
The require probability is
= 112 / 41664
= 1 / 372
= 0.002688
Brain Teaser No : 00010
In a contest of intelligence, three problems A, B and C were posed.
• Among the contestants there were 25 who solved at least one problem each.
• Of all the contestants who did not solve problem A, the number who solved B was twice the number who solved C.
• The number of participants who solved only problem A was one more than the number who solved problem A and at least
one other problem.
• Of all students who solved just one problem, half did not solve problem A.
How many students solved only problem B?
Answer
6 students solved only problem B
X => Students who solved only problem A
Y => Students who solved only problem B
Z => Students who solved only problem C
P => Students who solved both problem B and problem C
From 4 :
Students who solved only problem A = Students who solved only problem B + Students who solved only problem C
X = Y + Z
From 3 :
Students who solved problem A and at least one other = X - 1
From 2 :
(Y + P) = 2 * (Z + P)
Y + P = 2 * Z + 2 * P
Z = (Y - P) / 2
From 1 and Figure:
X + X - 1 + Y + Z + P = 25
2*X + Y + Z + P = 26
2*(Y + Z) + Y + Z + P = 26 (from 4)
3*Y + 3*Z + P = 26
3*Y + 3* (Y - P) / 2 + P = 26 (from 2)
6*Y + 3*Y - 3*P + 2*P = 52
9*Y - P = 52
Y = (52 + P) / 9
Now, it is obvious that all values are integer. Hence, P must be 2 and Y must be 6.
So 6 students solved only problem B.
Brain Teaser No : 00011
When Alexander the Great attacked the forces of Porus, an Indian soldier was captured by the Greeks. He had displayed such
bravery in battle, however, that the enemy offered to let him choose how he wanted to be killed. They told him, "If you tell a lie, you
will put to the sword, and if you tell the truth you will be hanged."
The soldier could make only one statement. He made that statement and went free. What did he say?
Answer
The soldier said, "You will put me to the sword."
The soldier has to say a Paradox to save himself. If his statement is true, he will be hanged, which is not the sword and hence
false. If his statement is false, he will be put to the sword, which will make it true. A Paradox !!!
Brain Teaser No : 00014
Five horses ran in the race.
• There were no ties.
• Sikandar did not come first.
• Star was neither first nor last.
• Mughal Glory came in one place after Sikandar.
• Zozo was not second.
• Rangila was two place below Zozo.
In what order did the horses finish?
Answer
It's simple.
Let's find the possible places horses can finish. Possibilities are:
Sikandar - 2,3,4 (not 5th as Mughal Glory came one place after him)
Star - 2,3,4
Mughal Glory - 3,4,5
Zozo - 1,3 (not 4th & 5th as Rangila is two place after him)
Rangila - 3,5
So the result is:
1 Zozo
2 Star
3 Rangila
4 Sikandar
5 Mughal Glory
Brain Teaser No : 00015
In the town called Alibaug, the following facts are true:
• No two inhabitants have exactly the same number of hairs.
• No inhabitants has exactly 2025 hairs.
• There are more inhabitants than there are hairs on the head of any one inhabitants.
What is the largest possible number of the inhabitants of Alibaug?
Answer
2025
It is given that no inhabitants have exactly 2025 hairs. Hence there are 2025 inhabitants with 0 to 2024 hairs in the head.
Suppose there are more than 2025 inhabitants. But these will violate the condition that "There are more inhabitants than there
are hairs on the head of any one inhabitants." As for any number more than 2025, there will be same number of inhabitants as
the maximum number of hairs on the head of any inhabitant.
Brain Teaser No : 00016
At what time after 4.00 p.m. is the minutes hand of a clock exactly aligned with the hour hand?
Answer
4:21:49.5
Assume that X minutes after 4.00 PM minute hand exactly aligns with and hour hand.
For every minute, minute hand travels 6 degrees.
Hence, for X minutes it will travel 6 * X degrees.
For every minute, hour hand travels 1/2 degrees.
Hence, for X minutes it will travel X/2 degrees.
At 4.00 PM, the angle between minute hand and hour hand is 120 degrees. Also, after X minutes, minute hand and hour hand
are exactly aligned. So the angle with respect to 12 i.e. Vertical Plane will be same. Therefore,
6 * X = 120 + X/2
12 * X = 240 + X
11 * X = 240
X = 21.8182
X = 21 minutes 49.5 seconds
Hence, at 4:21:49.5 minute hand is exactly aligned with the hour hand.
Brain Teaser No : 00017
A card contains following three sentences:
a. THIS SENTENCE CONTAINS FIVE WORDS.
b. THIS SENTENCE CONTAINS TWO VERBS.
c. EXACTLY ONE SENTENCE ON THIS CARD IS TRUE.
Is sentence C true or false?
Answer
It's a paradox.
You can’t say it true or false, as your answer will contradict itself.
Brain Teaser No : 00018
A barber in a certain small town shaves all the men who do not shave themselves, but never shaves any who do shave
themselves.
Does the barber shave himself? Note that the barber is a man.
Answer
It's a paradox.
You can't say it true or false, as your answer will contradict itself.
Brain Teaser No : 00021
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?
Answer
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
Manager = 5 coins