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Showing posts with the label brain teaser

Puzzle : Draw The Maximum Sum

Assume you are blindfolded and placed in front of a large bowl containing currency in $50, $20, $10, and $5 denominations. You are allowed to reach in and remove bills, one bill at a time. The drawing stops as soon as you have selected four-of-a-kind— four bills of the same denomination

What is the maximum sum of money you could accumulate before the drawing ends?


Draw The Maximum Sum


THIS should be the maximum sum! 

The Maximum That You Can Get!


What was the question?

The quick response to the question by any body would be 3 x 50 + 1 x 20 = $170 would be the maximum as next pick of highest currency of $50 will stop drawing of currencies. But that 5th attempt may not be of $50 & could be of $20,$10 or $5. So this case doesn't count those possibilities. This is worst case scenario where 3 out of 4 picks resulted into accumulation of 3 currencies of same denomination of $50.

So ideally, after drawing three $50 s, three $20 s, three $10 s, three $5 s and finally drawing one anything will stop drawing attempts as that will accumulate 4 bills of same denomination (of $50/$20/$10/$5). The best that can be picked is $50 to get the maximum.

That is total maximum of 50 x 3 + 20 x 3 + 10 x 3 + 5 x 3 + 50 = $305 can be accumulated in 12 attempts & stopping after 13th attempt. And this will be the best case.



The Maximum That You Can Get!

Spot The Liar Among

There is a party of 100 politicians. All of them are either honest or liars. You walk in knowing two things:

1. At least one of them is honest.


2. If you take any two politicians, at least one of them is a liar.


From this information, can you know how many are liars and how many are honest?


Spot The Liar Among


Know the total number of liars here! 

Knowing The Number of Liars


What is the question?

The information that we have - 

1. At least one of them is honest.

2. If you take any two politicians, at least one of them is a liar. 


Only one of them must be honest and other 99 must be liars. 

Those are the only numbers that can justify the second piece of information. In the case, if any 2 are selected at least 1 of them liar while other may or may not liar (i.e. may be honest). 


Knowing Number of Liars

Puzzle : The Password Challenge by Evil Troll

A bridge was guarded by an evil troll. The troll was very intelligent, but he was also a coward. He was afraid of anyone smarter than him. So every time anyone tried to cross the bridge, the troll would set up a test. If the traveler passed the test, he would be allowed to cross. Otherwise, the troll would eat him.

Three travelers, Al, Ben and Carl, came across the bridge. 

The troll told them, "You may only cross my bridge if you know the password." 
He wrote five three-letter words on a rock. The five words were HOE, OAR, PAD, TOE, and VAT.

He then said, "I will tell each of you a different letter from the password. If you know what the password is, I will let you pass. But don't tell anyone else your letter." 

He then whispered a letter from the password to each traveler so that neither of the other two could hear him.

Then the troll asked Al, "Do you know what the password is?" "Yes," said Al, and the troll let him pass.


Then the troll asked Ben, "Do you know what the password is?" "Yes," said Ben, and the troll let him pass.

 
Then the troll asked Carl, "Do you know what the password is?" "Yes," said Carl, and the troll let him pass.


So, what is the password?


THIS is the correct password! 

One more such challenge by an evil troll! 



Solution : Intelligent Response to an Evil Troll


What was the challenge?

The list of words given by evil troll is - 

HOE, OAR, PAD, TOE, and VAT

Remember, all travelers i.e. Al, Ben and Carl knew the correct password straightaway as soon as evil troll whispered a letter from the password to each traveler.

STEPS : 

1] The unique letters (i.e. letters appearing only once) in above list of words are D, H, P, R and V. The evil troll must have one of these letters to Al, as Al could guess the correct password straightaway. 

The word TOE doesn't have any unique letter, hence, TOE is eliminated straightaway. 

Had Evil troll whispered any letter from TOE (i.e. T, O or E), then Al wouldn't have an idea whether the correct password is TOE or VAT, HOE or TOE or OAR,  HOE or TOE.

2] Now, Ben is smart enough to know that TOE is eliminated from the race after Al's response. He has to think about only four words i.e. about HOE, OAR, PAD, VAT.

The unique letters appearing in rest of words list are D, E, H, P, R, T, and V. One of these letters must be with Al and other must be with Ben. 

But the word OAR has only one unique letter i.e. R. If OAR was the password then only 1 of 3 travelers would have guessed the password correctly while other 2 would have been confused.

Therefore, OAR can't be the password.

3] Carl too smart enough to recognize that OAR and TOE are not the correct passwords. So, he has to think of only 3 words -  HOE, PAD, VAT.

Here, unique letters from the list of words are - D, E, H, O, P, T, and V.

Every traveler must have one unique letter from the above list. In fact, the password itself must be formed by only unique letters from the above list.

Words PAD and VAT has only 2 unique letters ( P & D, V & T respectively).

So, if PAD or VAT was the correct password then the one with letter A wouldn't have been able to guess the correct password.

Hence, HOE must be the correct password. 

4] The letter H must be with Al as T, O, E can't be with him. Similarly, Ben can't have letter O, so he must had letter E and he knows TOE is not the password after hearing Al's response. And the letter O must be with Carl and he knows TOE or OAR are not the passwords.

Intelligent Response to an Evil Troll

Puzzle : An Evil Troll on A Bridge

A bridge was guarded by an evil troll. The troll was very intelligent, but he was also a coward. He was afraid of anyone smarter than him. So every time anyone tried to cross the bridge, the troll would set up a test. If the traveler passed the test, he would be allowed to cross. Otherwise, the troll would eat him.

A traveler came across the bridge. 


The troll said, "You may only cross my bridge if you know the password." 

He then wrote thirteen pairs of letters on a rock:

A-V
B-W
C-Q
D-M
E-K
F-U
G-N
H-P
I-O
J-R
L-X
S-T
Y-Z


"These thirteen pairs consist of all 26 letters of the alphabet," said the troll. 


"The password contains thirteen letters, no two of which are the same. Each pair consists of one letter that is in the password and one other letter. If you wrote out the "other" letters in alphabetical order and then wrote each "password" letter under each one's corresponding "other" letter, you would have the correct spelling of the password."

Then the troll wrote five short words on the rock: FACE, QUEST, QUICK, SWITCH, and WORLD. 


"Each short word contains exactly the same number of letters with the password," he said.

So, what is the password? 

Solution : An Evil Troll on A Bridge Puzzle : Solution


The thirteen pairs of letters given by an evil troll are -

A-V
B-W
C-Q
D-M
E-K
F-U
G-N
H-P
I-O
J-R
L-X
S-T
Y-Z


And 5 short words given by troll are -  FACE, QUEST, QUICK, SWITCH, and WORLD.  

As described in the given details, we'll refer letter from password as PASSWORD letter & other as OTHER letter.

As per troll, those short words are having same number of PASSWORD letters.

STEPS :

1] Both S & T are appearing in the pair with each other. Hence, either S or T must be a PASSWORD letter but not both. Since, both letters are appearing in short word QUEST, that is QUEST having at least 1 PASSWORD letter for sure hence, all 5 must have at least 1 PASSWORD letter.

2] Suppose every short word has 1 PASSWORD letter. With S or T as 1 PASSWORD letter from QUEST, other letters Q, U, E can't be PASSWORD letters. 

If Q, U, E are not PASSWORD letters then C (from C-Q pair), F (from F-U pair) and K (from E-K pair) must be PASSWORD letters. 

In that case, FACE will have 2 PASSWORD letters viz. C & E which goes against our assumption of having exactly 1 PASSWORD letter in each short word. 

3] Let's assume along with S or T the second PASSWORD letter is E i.e each short word has 2 PASSWORD letters. Again, Q, U can't be PASSWORD letters but C (from C-Q pair) & F (from F-U pair) must be. Still then FACE will have 3 PASSWORD letters which goes against our assumption of exactly 2 PASSWORD letter in each short word. 

4] Now, let's assume along with S or T the second PASSWORD letter is U. Again, Q, E can't be PASSWORD letters but C (from C-Q pair) & K (from E-K pair) must be. Still then QUICK will have 3 PASSWORD letters which goes against our assumption of exactly 2 PASSWORD letter in each short word. 

5] Let's assume there are 4 PASSWORD letters in each short word. So apart from S or T, the letters Q, U, E of short word QUEST must be PASSWORD letters. 

If Q, U, E are PASSWORD letters then C (from C-Q pair), F (from F-U pair) and K (from E-K pair) must NOT be the PASSWORD letters. 

In the case, the short word FACE will have maximum only 2 PASSWORD letters (not sure about A from A-V pair) which again goes against our assumption of exactly 4 PASSWORD letter in each short word. 

6] Hence, each short word must be having 3 PASSWORD letters. 

If Q, E are the PASSWORD letters with S or T in QUEST, then C & K can't be PASSWORD letters. With that, Q, U, I will be 3 PASSWORD letters in QUICK. And if U too is the PASSWORD letter then QUEST will have 4 PASSWORD letters. 

If Q, U are the PASSWORD letters with S or T in QUEST, then C & F can't be PASSWORD letters. With that, FACE can have maximum of only 1 PASSWORD letter. 

7] Hence, U & E must be other 2 PASSWORD letters apart from S or T in short word QUEST. So Q must not be the PASSWORD letter but C must be. Also, F and K can't be the PASSWORD letters.  Hence, FACE will have E, C and A as PASSWORD letters. 

If A is PASSWORD letter then V (from A-V pair) can't be the PASSWORD letter.

8] Next, from QUICK we will have, C, U and obviously I as 3 PASSWORD letters after Q, K are ruled out. If I is PASSWORD letter then O (from I-O pair) can't be the PASSWORD letter.

9] Just like QUEST, SWITCH too have either S or T as PASSWORD letter. Moreover, it has I & C as PASSWORD letters. Hence, H & W must not be the PASSWORD letters.

10] So, if W & O are not the PASSWORD letters then other 3 letters of WORLD i.e. R, L, D must be PASSWORD letters. With that M (from D-M pair), J (from J-R pair) and X (from L-X pair) are ruled out.

11] So far we have got - 

PASSWORD letters - U, E, C, A, I, R, L, D, Either S or T.

OTHER letters - Q, F, K, V, O, H, W, M, J, X  

12] Arranging every OTHER letter in alphabetical order & writing down corresponding PASSWORD letter below it -

OTHER :  F   H   J   K   M   O   Q   V   W   X
PASS.  :  U   P   R   E   D   I    C   A    B   L 

13] Now, S-T, G-N, Y-Z are the only 3 pairs left. And correct placement for these pairs must be like.

OTHER :  F   G   H   J   K   M   O   Q   S   V   W   X   Z
PASS.  :  U   N   P   R   E   D   I    C   T   A    B    L   Y

CONCLUSION : 

The PASSWORD that an evil troll has set must be UNPREDICTABLY

An Evil Troll on A Bridge Puzzle : Solution
 
 

Puzzle : "Who Stole My Purse?"

An elementary school teacher had her purse stolen. The thief had to be Lilian, Judy, David, Theo, or Margaret. When questioned, each child made three statements: 

Lilian:
(1) I didn’t take the purse.
(2) I have never in my life stolen anything.
(3) Theo did it. 


Judy:
(4) I didn’t take the purse.
(5) My daddy is rich enough, and I have a purse of my own.
(6) Margaret knows who did it. 


David:
(7) I didn’t take the purse.
(8) I didn’t know Margaret before I enrolled in this school.
(9) Theo did it. 


"Who Stole My Purse?"


Theo:
(10) I am not guilty.
(11) Margaret did it.
(12) Lillian is lying when she says I stole the purse. 


Margaret:
(13) I didn’t take the teacher’s purse.
(14) Judy is guilty.
(15) David can vouch for me because he has known me since I was born. 


Later, each child admitted that two of his statements were true and one was false. Assuming this is true, who stole the purse?

Here is name of the thief! 

"Finally Got My Stolen Purse!"


How it was stolen?

Let's recollect all the statements given by all accused.

Lilian:
(1) I didn’t take the purse.
(2) I have never in my life stolen anything.
(3) Theo did it. 


Judy:
(4) I didn’t take the purse.
(5) My daddy is rich enough, and I have a purse of my own.
(6) Margaret knows who did it. 


David:
(7) I didn’t take the purse.
(8) I didn’t know Margaret before I enrolled in this school.
(9) Theo did it. 


Theo:
(10) I am not guilty.
(11) Margaret did it.
(12) Lillian is lying when she says I stole the purse. 


Margaret:
(13) I didn’t take the teacher’s purse.
(14) Judy is guilty.
(15) David can vouch for me because he has known me since I was born. 


Let's not forget that 2 of 3 statements made by each student are true & other is false.

Now, Theo says he is innocent in his 2 statements - (10) and (12). Since, 2 of his statements are true then (10) and (12) must be true. Hence, Theo is really innocent in case.

If Theo is innocent then both (3) and (9) are lie.

If (9) is lie, then other 2 statement of David i.e. (7) and (8) are true. If (8) is true then (15) must be lie. 

And if (15) is lie then both (13) [lie in (12) also suggests same] and (14) must be true. 

Hence, as per (14), Judy is guilty who has stolen the purse. 

"Finally Got My Stolen Purse!"


Puzzle : The Story of 3 Dragons

I met three dragons. One always tells the truth, other one always lies and the last one alternates between lie and truth.

Dragon 1: You may ask us one question, then you must guess which dragon is which

Dragon 2: He’s lying. You may get three questions

Dragon 3: Oh no. It’s definitely one question

I asked the first dragon a question

Me: What would the second dragon say if I were to ask it if the 3rd dragon had been lying when it agreed with the first one that I could ask only one question

Dragon 1: He’d say, “Yes, the 3rd dragon was lying”

Then I asked a second question addressing the three dragons…… But they remained silent.

And, I solved the puzzle in 90 sec.


So, which dragon is which?


The Story of 3 Dragons

Know the TRUTH of each dragon here! 

Solution : Inside The Story of 3 Dragons


What was the story?

Let's see what are key statements in the story once again.

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

Dragon 1: You may ask us one question, then you must guess which dragon is which.

Dragon 2: He’s lying. You may get three questions.

Dragon 3: Oh no. It’s definitely one question.

I asked the first dragon a question.

Me: What would the second dragon say if I were to ask it if the 3rd dragon had been lying when it agreed with the first one that I could ask only one question?

Dragon 1: He’d say, “Yes, the 3rd dragon was lying”

Then I asked a second question addressing the three dragons…… But they remained silent.

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

On second question, they remained silent clearly indicates that only 1 question was allowed to ask. Hence, Dragon 2 must be lying for sure.

After knowing the fact that Dragon 2 lied in it's first statement, we know that first statements of Dragon 1 and Dragon 3 are true. 

Now, there are 2 cases possible for Dragon 1 and Dragon 3.

CASE 1 : Dragon 1 speaks alternate and Dragon 3 always tells the truth.

That means the Dragon 1 should lie in it's next statement given in response of my question. 

If Dragon 3 is always telling the truth, the Dragon 2 will always say that Dragon 3 is liar. 

Let's simplify my question to the Dragon 1 as - 

"What will Dragon 2 say if I ask it whether Dragon 3 is lying?" 

Now as per our logic the Dragon 1 should lie in response as - 

Dragon 1: He’d say, “Nope, the 3rd dragon is telling the truth” 

This is contradictory the actual response given by Dragon 1 to the question - 

"What will Dragon 2 say if I ask it whether Dragon 3 is lying?" 

Dragon 1: He’d say, “Yes, the 3rd dragon was lying”

Hence, assumption that Dragon 1 speaks alternate and Dragon 3 tells the truth goes wrong here.

CASE 2 : Dragon 1 tells the truth and Dragon 3 speaks alternate.

That means Dragon 1 will tell truth in response to my question. Since, Dragon 3 is telling truth in it's first statement the always lying Dragon 2 will say that Dragon 3 is lying if asked about Dragon 3.

This is the truth that Dragon 1 tells us in response to my question as - 

"What will Dragon 2 say if I ask it whether Dragon 3 is lying?" 

Dragon 1: He’d say, “Yes, the 3rd dragon was lying”

Hence, this assumption i.e. Dragon 1 tells the truth and Dragon 3 speaks alternate should be correct.

To conclude, Dragon 1 is telling the truth, Dragon 2 always lies and Dragon 3 speaks alternate 
 
Inside The Story of 3 Dragons



Puzzle: A Visit to the Casino!

There is a casino and it has 4 gates, let say A, B, C and D

Now the condition is that every time you enter casino you have to pay $5 and every time you leave the casino, you again have to pay $5. Also, whenever you enter the casino whatever amount you have with you will get double.

Now you enter the casino through gate A and come out through gate B, again you go inside casino from gate C and come out of gate D, at the end of this process you should be left with no money

So calculate how much money you should carry with you when you enter the Casino?

A Visit to the Casino!


THIS should be the amount that you need to carry... 

Solution: Amount Needed for a Casino Visit


What is the puzzle?

Let's suppose you have amount 'x' initially in your wallet.

1. On paying $5 for entry at gate A amount left is x - 5 .

2. After entry into the casino it double and becomes 2 ( x - 5 ) = 2x - 10.

3. For exit at gate B you pay $5 and the amount left with you is 2x - 10 - 5 = 2x - 15.

4. Again, for the entry at gate C, you pay $5 more. So the amount with you will be  - 
    2x - 15 - 5 = 2x - 20.

5. The amount is doubled to become 2(2x - 20) = 4x - 40 after the entry into casino.

6. Now, you have to pay $5 one more time to have exit via gate D. Hence, the amount 
left will be 4x - 40 - 5 = 4x - 45.

7. As per given condition, the amount that you should have on exit must be 0.

Hence, 4x - 45 = 0 i.e. 4x = 45. Therefore, x = 11.25. 

So you should carry $11.25 before you enter into the casino to have $0 after exit out of the casino.

Amount Needed for a Casino Visit


Let's verify this one with the amount at each of stages above.

1. Amount = 11.25 - 5 = 6.25

2. Amount = 2 x 6.25 = 12.50

3. Amount = 12.50 - 5 = 7.50

4. Amount = 7.50 - 5 = 2.50

5. Amount = 2 x 2.50 = 5 

6. Amount = 5 - 5 = 0

7. Amount = 0
    

Puzzle : Who Stole Which Animal

A horse, a donkey and a camel were stolen.

Three suspects: Robert, Scott and Tommy. All we know that each person stole one animal, but we do not know who stole which. Here are the investigation statements.


Robert: Tommy stole the horse.

Scott: Tommy stole the donkey.


Tommy: They both were lying. I did not steal the horse or the donkey.


Later on, police found out =>

The man who stole the camel told a lie.


The man who stole the horse told the truth.


Can you find out who stole which?

Puzzle : Who Stole Which Animal



Here is SOLUTION of the puzzle! 

Source

Solution : Who Stole Which Animal Puzzle


What was the puzzle?

Take a look at the statements of three suspects first - 
------------------------------------------------------------

Robert: Tommy stole the horse.

Scott: Tommy stole the donkey.


Tommy: They both were lying. I did not steal the horse or the donkey.


------------------------------------------------------------
 
And what the police found after investigation - 

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

1. The man who stole the camel told a lie.

2. The man who stole the horse told the truth.


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

1. If the Robert is one who stole the HORSE then his statement must be TRUE where he say Tommy is the HORSE thief. 

If there are 2 person who stole the HORSE then Scott must have stolen 2 animals i.e. CAMEL and DONKEY. But as per given data, each person stole only 1 animal.

Hence, Robert can't be a HORSE thief.

2. Assuming Tommy is a HORSE thief & thereby taking his statement as TRUTH. But the assumption itself contradicts claim made by him in his statement where he says he didn't steal the HORSE. 

That is, Tommy too can't be a HORSE thief.

3. Only leftover suspect is Scott who must have stolen HORSE. And his statement must be TRUE. 

That means, Tommy has stolen the DONKEY and hence, Robert must be a CAMEL thief.  

Puzzle : Who Stole Which Animal - SOLUTION

Puzzle : And Escape Story of Robbers Continues


Where story begins?

Babylas, Hilary, and Sosthenes have escaped the tower and divided their treasure into three bags. But now they must cross a river, and the boat can accommodate only two men at a time, or one man and a bag. None will trust another with his bag on the shore, but they agree that a man in the boat can be trusted to drop or retrieve a bag at either shore, as he’ll be too busy to tamper with it.



 How can they cross the river?


 

Solution: Robbers' Planned Journey Across the River


Let's recall that the boat can accommodate only two men at a time, or one man and a bag.

1. Sosthenes takes his bag across the river leaves it at other shore & comes back.

2. Sosthenes takes Hilari's bag to the other shore & leaves it there where his own bag is already there. 


Robbers' Planned Journey Across the River

3. Now, Hilari takes Sosthenes to the other shore, leaves him there & come back after recollecting own bag.


Robbers' Planned Journey Across the River

4. Hilari drops own bag at near shore & takes Babylas to other shore & returns back.


Robbers' Planned Journey Across the River

5. Next, he takes Babylas's bag & drops it at other shore where Babylas is waiting for his bag. And Hilary returns once again.

6. Finally, he collects his own bag and takes it to other shore.


Robbers' Planned Journey Across the River

Maze Challenge For a Rat?

A rat is placed at the beginning of a maze and must make it to the end. There are four paths at the start that he has an equal chance of taking: path A takes 5 minutes and leads to the end, path B takes 8 minutes and leads to the start, path C takes 3 minutes and leads to the end, and path D takes 2 minutes and leads to the start.

What is the expected amount of time it will take for the rat to finish the maze?



Maze Challenge For a Rat?


This could be the average time that rat needed!
 

A Rat Finishing off The Maze!


The challenge ahead of rat?

For rat, there are 2 paths viz A (5 minutes) and C (3 minutes) leading to the end while paths B (8 minutes) and D (2 minutes) lead to the start again.

Since, there are 4 paths & each having equal chance of being chosen by rat, there is 1/4 th chance for each path for to be chosen by rat.

Let's assume T be the time needed for rat to finish the maze. 

But if rat selects path B or D then rat need T more time again as these paths lead to the start of the maze again.

Hence,

T = (1/4) x A + (1/4) x B + (1/4) x C + (1/4) x D

T =  (1/4) x 5 + (1/4) x (8 + T) + (1/4) x 3 + (1/4) x (2 + T)

T = (5/4) + (2) + (T/4) + (3/4) + (1/2) + (T/4)

T =  (9/2) + (T/2)

T/2 = 9/2

T = 9

That is rat needs 9 minutes to finish the maze. 

A Rat Finishing off The Maze!
 
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