Who is The Opposite Gender?

Sam, Alex, Charlie, and Jordan are related. 

One of them is the opposite gender from the other three. Here are some facts:

1. Charlie's only son is either Sam or Alex.

2. Jordan's sister is either Alex or Charlie.

3. Jordan is either Sam's brother or Sam's only daughter.

Who is the opposite gender from the other three?

Know here the name of the person with opposite gender! 

Charlie is The Opposite Gender!

What was the puzzle?

Given Facts : 

Sam, Alex, Charlie, and Jordan are related


1. Charlie's only son is either Sam or Alex.
2. Jordan's sister is either Alex or Charlie.
3. Jordan is either Sam's brother or Sam's only daughter.

ANALYSIS : 

1] As per (3), if Jordan is Sam's only daughter then Jordan must not have any sister. But this is opposite to the fact (2). Therefore, Jordan must be Sam's brother. Jordan is male for sure. 

2] If Jordan's sister is Alex (female), then as per (1), Charlie's only son (male) must be Sam. But as concluded above [1], Jordan is Sam's brother so how Charlie can have only one son? Therefore, Jordan's sister is Charlie who is obviously female.

3] If Jordan is Sam's brother [1] and Charlie is Jordan's sister then it's clear that Jordan, Sam and Charlie are siblings. And now as fact (1) suggests Charlie's only son must be Alex (male).

CONCLUSION : 

ALEX, JORDAN and SAM are male and CHARLIE is the opposite gender i.e. female. 

  

The Thanksgiving Pageant

Allison, Jerry, Bonnie, and Bill are participating in a Thanksgiving Pageant at their school. 

The students will portray an Indian warrior, a pilgrim, an Indian maiden, and a deer. Their props consist of a pumpkin, a fish, a basket of corn, and colored leaves. During the pageant, they will recite a poem, sing a song, do a dance, and act as the narrator. Their parents, whose lasts names are Lee, Newton, Myers, and Schuler, will be watching in the audience. The ages of the performers are 13, 12, 11, and 10 years old. 

Use the clues to help you find out who will be doing what for the pageant.

1. Mrs. Lee made her daughter's costume and also the costumes of the Indian maiden and the dancer. 

2. Mr. Myers helped his son rehearse his poem. 

3. The dancer was older than Lee and the pilgrim, but younger than Allison. 

4. The 11-year-old ripped her deer outfit, but her mother pinned it.

5. Newton carried his fish during his tribal dance.

6. Jerry's pumpkin was a symbol of the feast for the pilgrims. 

7. The Indian maiden carried corn as she sang the song of feasting.

Simplified Solution Here! 

Little Performers at The Thanksgiving Pageant

What was the puzzle?

Given Data : 

STUDENTS     : Allison, Jerry, Bonnie, Bill

CHARACTERS : Indian warrior, Pilgrim, Indian maiden, Deer

PROPS           : Pumpkin, Fish, Basket of corn, Colored leaves

ACT                : Poem, Song, Dance, Narrator

LAST NAMES  : Lee, Newton, Myers, Schuler

AGE                : 13, 12, 11, 10

Given Clues : 

1. Mrs. Lee made her daughter's costume and also the costumes of the Indian maiden and the dancer. 

2. Mr. Myers helped his son rehearse his poem. 

3. The dancer was older than Lee and the pilgrim, but younger than Allison. 

4. The 11-year-old ripped her deer outfit, but her mother pinned it.

5. Newton carried his fish during his tribal dance.

6. Jerry's pumpkin was a symbol of the feast for the pilgrims. 

7. The Indian maiden carried corn as she sang the song of feasting.

STEPS :

First of all let's make a table like below & fill it as per clues.

1]  As per clue (1), student having last name Lee, an Indian maiden and dancer are three different students.

2] As per (3), the dancer must be 12 years old with Lee and Pilgrim having age 10 & 11 but order yet to be known. With that Allison must be 13 years old. This clue also suggests that the dancer or Lee isn't pilgrim.

3] The clue (5) clearly suggest that Newton is dancer carrying fish as a property. Also, clue (6) suggests Jerry is pilgrim having pumpkin. And clue (7) suggests that, Indian Maiden sung a song while carrying a basket of corn.

4] With that, we can conclude that Lee must be carrying colored leaves. Also, the clue (4) must be pointing at Lee now. So Lee is 11 years old wearing deer outfit.

5] It's clear now that Newton is Indian Warrior. And, 10 years old (STEP 2) Jerry is Myers who father helped him to rehearse his poem as per clue (2).

6] Since Allison is 13 years old, she must be Indian Maiden carrying a basket of corn while singing a song. She must have last name Schuler - the only last name left. Since (1) suggests Lee is girl, her name must be Bonnie who is narrator carrying a colored leaves. Finally, first name of Newton must be Bill.

7] So, the final table looks as - 

Challenge of Father to Son

A man told his son that he would give him $1000 if he could accomplish the following task. 

The father gave his son ten envelopes and a thousand dollars, all in one dollar bills. He told his son, "Place the money in the envelopes in such a manner that no matter what number of dollars I ask for, you can give me one or more of the envelopes, containing the exact amount I asked for without having to open any of the envelopes. If you can do this, you will keep the $1000."

When the father asked for a sum of money, the son was able to give him envelopes containing the exact amount of money asked for. 

How did the son distribute the money among the ten envelopes?

THIS is how son accepts the challenge!

Son's Response to the Father's Challenge

What was the challenge?

For a moment, let's suppose father had given $30 to son and provided 5 envelopes and put the same challenge.
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Here, use of the binary number system helps in matter.

The son would distribute 15 dollars into 4 envelops like - 

2^0 = 1, 2^1 = 2, 2^2 = 4, 2^3 = 8.

Now, for any amount asked between 1 to 15, son can produce some of these 4 envelops wherever 1 is there in envelop column for that particular amount.

For example, if father asks for $10 (Binary - 1010), son would give envelop 4 and 2 (8+2=10).

After putting $15 dollar in 4 envelops, he puts remaining $15 in 5th envelop so that he can cover rest of amount between 16 to 30.

If father asks amount greater than 15 then he would take envelop of $15 first and depending on how much the amount asked is greater than this $15 he would pick some of those 4 envelops.

For example, if father asks for $24, then he picks envelop 5 having $15 and envelops for amount 24 - 15 = 9 (Binary - 1009) i.e. envelop 4 and 1 (8+1=9)  i.e. total of 15 + 9 = 24.

So, what we observe from this is that the number of envelops needed for such arrangement is equal to the number of binary bits needed to represent the amount itself or nearest power of 2 greater than the amount.

In above case, to represent 30 in binary we need 5 bits or nearest power of 2 greater than 30 is 32 which needs 5 bits for representation.

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Now, let's turn to the actual challenge where father has asked son to distribute $1000 rightly in 10 envelopes. 

The reason for selecting 10 as a number of envelops is clear now as 1000 needs 10 bits in binary or nearest power of 2 greater than 1000 is 1024 which needs 10 bits for binary representation.

So, the son puts 256, 128, 64, 32, 16, 8, 4, 2, 1 dollars in 9 envelops (envelop numbered as Envelop 9, Envelop 8.........Envelop 1 in order)
 and 1000 - 511 = 489 dollars in 10th envelop.

First 9 envelops will cover amounts from 1 to 511 and for amounts greater than 511 inclusion of 10th envelop having 489 dollars is mandatory.

Again selection of envelops for the amount 511 to 1000 depends on how much the amount exceeds the $489. The binary representation of that difference and selection of envelop accordingly is all that needed.
 
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Let's make sure this distribution with couple of examples.

If father asks for amount of $109 (binary - 1101101) then son picks 

Envelop 1($1) + Envelop 3 ($4) + Envelop 4 ($8) + Envelop 6 ($32) + 
Envelop 7 ($64) i.e. having amount = 1 + 4 + 8 + 32 + 64 = 109 dollars.

If father asks for $525 then son gives $489 via Envelop 10 and rest of amount 
530 - 489 = 40 (Binary - 101000) in form of Envelop - 6 ($32) and Envelop 4 ($8).   

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Who Did It: Murder in A Family of 4

One evening there was a murder in the home of married couple, their son and daughter. One of these four people murdered one of the others. One of the members of the family witnessed the crime.The other one helped the murderer.

These are the things we know for sure:

1. The witness and the one who helped the murderer were not of the same sex.

2. The oldest person and the witness were not of the same sex.

3. The youngest person and the victim were not of the same sex.

4. The one who helped the murderer was older than the victim.

5. The father was the oldest member of the family.

6. The murderer was not the youngest member of the family.

Who was the murderer?

   
Find out the murderer here!

Source 

Roles of Family Members

What was the case?

From (6), we know the youngest one wasn't the murderer. Clue (3) suggests youngest wasn't the victim & (4) hints that youngest wasn't helper too. Hence, youngest must be witness.

So possibilities of others' role are listed in table below.

 

From (2), the witness had opposite sex than the oldest & from (5), we know father is the oldest. So witness must be daughter.

From (4), murderer was older than victim & since father is oldest he can't be victim. So last 2 possibilities are eliminated.