What day of the week is it?

A group of campers have been on vacation so long, that they've forgotten the day of the week. 

The following conversation ensues. 

Darryl: "What's the day? I don't think it is Thursday, Friday or Saturday." 

Tracy: "Well that doesn't narrow it down much. Yesterday was Sunday." 

Melissa: "Yesterday wasn't Sunday, tomorrow is Sunday." 

Ben: "The day after tomorrow is Saturday." 

Adrienne: "The day before yesterday was Thursday." 

Susie: "Tomorrow is Saturday." 

David: "I know that the day after tomorrow is not Friday." 

If only one person's statement is true, what day of the week is it?

So it was THIS day of the week!

The Forgotten Day of Week is Wednesday!

What was the puzzle?

Let's see once again the conversation that campers had - 

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Darryl: "What's the day? I don't think it is Thursday, Friday or Saturday." 

Tracy: "Well that doesn't narrow it down much. Yesterday was Sunday." 

Melissa: "Yesterday wasn't Sunday, tomorrow is Sunday." 

Ben: "The day after tomorrow is Saturday." 

Adrienne: "The day before yesterday was Thursday." 

Susie: "Tomorrow is Saturday." 

David: "I know that the day after tomorrow is not Friday."

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Let's see what day statement of each is suggesting -

Darryl - Sunday, Monday, Tuesday, Wednesday.

Tracy - Monday.

Melissa - Saturday.

Ben - Thursday.

Adrienne - Saturday.

Susie - Friday.

David - Sunday, Monday, Tuesday, Thursday, Friday or Saturday.  

If we assume David's statement is TRUE then one of statements of Darryl (Sunday, Monday, Tuesday are common) or Tracy (Monday is common) or Melissa & Adrienne (Saturday is common) or Susie (Friday is common) or Ben (Thursday is common) has to be also TRUE. But this is against the given data that only 1 of the statement is TRUE.

Hence, David's statement must be FALSE and the only day that isn't pointed by David is Wednesday.

So the day must be Wednesday as suggested correctly by Darryl and thereby making statements of every other camper including David FALSE. 

A New Word Every Day!

During a six-day period from Monday through Saturday, Eliza Pseudonym and her friends Anna, Barbra, Carla, Delilah, and Fiona have subscribed to an internet mailing list that features a new word every day. 

No two women subscribed on the same day. On each day during the six-day period, a different word has been featured (abulia, betise, caryatid, dehisce, euhemerism, and floruit, in some order). 

From the clues below, determine the day on which each woman subscribed, and the day on which each word was featured.

1. Exactly one of the women has a name beginning with the same letter of the alphabet as the word featured on the day that she subscribed to the mailing list.

2. The word "caryatid" was featured precisely two days prior to Fiona joining the mailing list.

3. Carla joined the mailing list on Friday.

4. Anna signed up for the mailing list precisely one day after the word "euhemerism" was highlighted.

5. Wednesday's word did not end with the letter "e".

6. Barbra subscribed precisely three days after the word "dehisce" was featured.

Here is every word of woman of the day! 

Assigned Word to the Woman of the Day

What was the challenge?

As we know, Eliza Pseudonym and her friends Anna, Barbra, Carla, Delilah, and Fiona have subscribed to an internet mailing list that features a new word every day. No two women subscribed on the same day. On each day during the six-day period, a different word has been featured (abulia, betise, caryatid, dehisce, euhemerism, and floruit, in some order).

And given clues are - 

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1. Exactly one of the women has a name beginning with the same letter of the alphabet as the word featured on the day that she subscribed to the mailing list.

2. The word "caryatid" was featured precisely two days prior to Fiona joining the mailing list.

3. Carla joined the mailing list on Friday.

4. Anna signed up for the mailing list precisely one day after the word "euhemerism" was highlighted.

5. Wednesday's word did not end with the letter "e".

6. Barbra subscribed precisely three days after the word "dehisce" was featured.

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Let's make a table like below and fill it one by one as per clues.

 STEPS :  

1] As per (3), Carla joined the mailing list on Friday. And as per (6), Barbra's subscription day must be Thursday, Friday or Saturday with word 'dehisce' on Monday or Tuesday or Wednesday. 

But as per (5), ''dehisce'' can't be on Wednesday and Carla has already joined on Friday, hence Barbra must have joined on Thurday with word "dehisce" featured on Monday.

2] Only possible location for "caryatid" and Fiona for (2) to be true are Thursday and Saturday respectively. That's because Monday is already 'occupied' by "dehisce" so Fiona can't be on Wednesday. And as we can see, Thursday and Friday already 'occupied' by Barbra and Carla.

3] With that, for (4) to be true, only possible location for "euhemerism" is Tuesday and for Anna is Wednesday.

4] As per (1), Delilah and Eliza can't be on Monday & Tuesday at a time as that will violate (1). Therefore, Delilah must be on Tuesday and Eliza on Monday.

 
5] As per (5), "betise can't appear on Wednesday. 

Suppose it appears on Friday. 

CASE 1 : The word "abulia" with Anna on Wednesday & "floruit" with Fiona on Saturday. This violates (1), as there would be 2 women have names beginning with the same letter of the alphabet as the word featured on the day that she subscribed to the mailing list.

CASE 2 :  The word "floruit" with Anna on Wednesday & "abulia" with Fiona on Saturday. Again, this is against (1), as there is no woman has a name beginning with the same letter of the alphabet as the word featured on the day that she subscribed to the mailing list.

Therefore, "betise" must be appearing on Saturday, "floruit" on Friday and "abulia" on Wednesday with Anna.

CONCLUSION :

The final table looks like -

The Apple Conundrum

Two women are selling apples. The first sells 30 apples at 2 for $1, earning $15. The second sells 30 apples at 3 for $1, earning $10. So between them they’ve sold 60 apples for $25.

The next day they set the same goal but work together. They sell 60 apples at 5 for $2, but they’re puzzled to find that they’ve made only $24.

What became of the other dollar?

Here, could be that lost dollar! 

Behind The Apple Conundrum

What is the conundrum?

They sell 60 apples at 5 for $2, that means 12 such sets of 5 apples. Suppose, out of each such set, 1 woman takes out $1 for 2 apples and other takes $1 for 3 apples. So, first woman earns $12 by selling 24 apples and second woman sells 36 apples for $12.

In short, first woman gives away 6 apples (from her 30 apples) to second woman increasing her count to 36 reducing her own count to 24. First woman would have made $3 from those but second woman only made $2 from those 6 apples. And there is that lost dollar in earning.

So, 60 apples can't be divided equally to find the earning as they had sold apples at different rates on previous day.

Other way, if they wanted to sell apples together with 30 apples each, then they should have sold apples at average of (1/2 + 1/3)/2  = $5/12 per apple (i.e. 12 apples for $5) instead of $2/5 per apple.

The difference in price per apple (5/12 - 2/5) = (1/60).

So the difference in earning after selling 60 such apples = (1/60) x 60 = 1.

And there is that other dollar! 

What's wrong gone here on next day? Instead of averaging dollars per apple, apples per dollar are added directly which resulted reduced cost of each apple. 

Interesting Fact of Handshake Count

Suppose we fill Yankee Stadium with 50,000 people and ask them to spend the day shaking hands with one another.

Prove that, at the end of the day, at least two participants will have shaken hands with the same number of people.

Click here for proof!

Proving Interesting Fact of Handshake Count

What was that fact?

Let's contradict the given fact & assume no 2 people have same number of handshakes. In that case, the most gregarious person would have 49999 handshakes & next gregarious person would shake hands with 49998 people and so on. 

This way, the shyest person should have 0 shake hands. But the most gregarious guy must have had handshake with this shyest guy as his count of 49999 also includes this shyest guy. So this is impossible case.

Hence, at least 2 participants would have shaken hands with the same number of people.

 
In other way, the most shyest participant would have 1 handshake, next shyer guy would have 2 & so on. The more gregarious would have 49999 handshakes that includes the shake hand with the most gregarious person. Now, most gregarious person is bound to have 49999 handshakes as he/she can't have 50000 as there are only 50000 people in the stadium including himself/herself. 

That's why, at least 2 participants would have shaken hands with the same number of people.

The Dice Date Indicator!

How can you represent days of month using two 6 sided dice? You can write one number on each face of the dice from 0 to 9 and you have to represent days from 1 to 31, for example for 1, one dice should show 0 and another should show 1, similarly for 29 one dice should show 2 and another should show 9.

This is how it can be indicated!

Making of The Dice Date Indicator

What was the challenge?

Dice 1: 0 1 2 3 5 7

Dice 2: 0 1 2 4 6 8

The number 0 has to be present on both the dice. The '0' on first die needed for dates from 1 to 9 to show them as 01,02,03......and the '0' on second die will be used for the dates 10,20,30.

The number 1 and 2 are repeated on the dates 11 and 22 so those 2 numbers has to be there on both dice.

Now, we are left with total 6 positions but 7 numbers - 3 to 9.

However, 6 and 9 can be represented by single die if it is written on one of the side of the die. In normal position it will represent 6 & in inverted position it will show 9 or say vice versa.

For example, the dates 6 and 9 can be indicated as - 

Journey In Parts

Someone drove from Aardvark to Beeville.

On the first, day they traveled 1/3 of the distance.

On day two, they traveled 1/2 of the remaining distance.

On day three, they traveled 2/3 of the remaining distance.

On day four, after covering 3/4 of the remaining distance, they were still 5 miles away from Beeville.

How many miles had they covered so far?

Know the total distance traveled!
 

Total Distance In The Journey

Click for the question! 

We need to start in reverse.

In last part after covering 3/4 still 5 miles left which accounts for 1/4 of remaining distance. Hence, 20 miles were left at the start of DAY 4.

On DAY 3, 2/3rd covered leaving 20 miles for DAY 4. That means 20 miles distance is remaining 1/3rd. Hence, at the start of DAY 3, 60 miles were left.

On DAY 2, 1/2 of covered leaving 60 miles for DAY 2. So that means 60 miles distance is remaining 1/2. So at the start of DAY 2, 120 miles yet to be covered.

On DAY 1, 1/3 of covered leaving 120 miles for DAY 2. Meaning 120 miles distance is remaining 2/3. Hence, 180 miles yet to be covered at the start of DAY 1.

Out of 180 miles, 175 covered in 4 days still 5 miles left.