Solution : The Logical Team Work

What was the puzzle?

Let's number the first person from where the drive starts counting first as 1. So there are 30 people standing in circle and we have numbered them in clockwise direction. 

Remember, driver starts counting another nine starting from where he stopped to give a moment for 9th person to leave.

Let's divide the elimination process into rounds.

In every round of driver's counting few fans will be eliminated as below.

Round 1 - 

Counting starts clockwise from 1, 10 and 19,

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30

Fans standing at 9, 18 and 27 are asked to leave. 

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30

Total eliminations after Round 1 = 3.

Round 2 -

Counting started from 28, 7 and 17,

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30

Those who are standing at 6, 16 and 26 have to start walking. 

1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30

Total eliminations after Round 2 = 6. 

Round 3 - 

Counting starts with 28, after 9 counts it starts with 8 & it resets when 19 is eliminated,

1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30

People standing at 7, 19 and 30 need to leave.

1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 14, 15, 17, 20, 21, 22, 23, 24, 25, 28, 29

Total eliminations after Round 3 = 9.  

Round 4 - 

Counting starts with 1 and after 9 counts it starts with 13, 

1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 14, 15, 17, 20, 21, 22, 23, 24, 25, 28, 29 

Here, persons at 12 and 24 should leave. 

1, 2, 3, 4, 5, 8, 10, 11, 13, 14, 15, 17, 20, 21, 22, 23, 25, 28, 29 

Total eliminations after Round 4 = 11.  

Round 5 - 

Now, Counting starts with 25 and after 9 counts it starts with 10, 

1, 2, 3, 4, 5, 8, 10, 11, 13, 14, 15, 17, 20, 21, 22, 23, 25, 28, 29

That is persons at 8 and 22 need to start walking. 

1, 2, 3, 4, 5, 10, 11, 13, 14, 15, 17, 20, 21, 23, 25, 28, 29 

Total eliminations after Round 5 = 13.  

Round 6 -  

Counting starts with 23 and after 9 counts it starts with 10, 

1, 2, 3, 4, 5, 10, 11, 13, 14, 15, 17, 20, 21, 23, 25, 28, 29  

Obviously, fans standing at 5 and 23 have to leave. 

1, 2, 3, 4, 10, 11, 13, 14, 15, 17, 20, 21, 25, 28, 29

Total eliminations after Round 6 = .  15

That's it! Now, driver can easily drive those remaining 15 fans to the football stadium.    

CONCLUSION : 

You should arrange your teammates to the below positions in order to save them from elimination process - 

 1, 2, 3, 4, 10, 11, 13, 14, 15, 17, 20, 21, 25, 28, 29.

Puzzle : Which one is the car thief?

A car thief, who had managed to evade the authorities in the past, unknowingly took the automobile that belonged to Inspector Detweiler. 

The sleuth wasted no time and spared no effort in discovering and carefully examining the available clues. He was able to identify four suspects with certainty that one of them was the culprit.

The four make the statements below. In total, six statements are true and six false.

Suspect A:

1. C and I have met many times before today.
2. B is guilty.
3. The car thief did not know it was the Inspector's car.

Suspect B:

1. D did not do it.
2. D's third statement is false.
3. I am innocent.

Suspect C:
 
1. I have never met A before today.
2. B is not guilty.
3. D knows how to drive.

Suspect D:
 
1. B's first statement is false.
2. I do not know how to drive.
3. A did it.

Which one is the car thief?

Know here who is that car thief? 

Solution : The Unlucky Car Thief

What was the puzzle?

Take a look at the statements made by suspects.

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Suspect A:

1. C and I have met many times before today.
2. B is guilty.
3. The car thief did not know it was the Inspector's car.

Suspect B:

1. D did not do it.
2. D's third statement is false.
3. I am innocent.

Suspect C:

1. I have never met A before today.
2. B is not guilty.
3. D knows how to drive.

Suspect D:

1. B's first statement is false.
2. I do not know how to drive.
3. A did it.

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After investigation, it is found that,  in total, six statements are true and six false.

We will name statements as A1 for first statement of A, A2 for his second statement, B1 for B's first statement B2 for his second statement and so on.

1. Since, a car thief, who had managed to evade the authorities in the past, unknowingly took the automobile that belonged to Inspector Detweiler, we assume statement A3 is TRUE.

2. A1 and C1, C3 and D2 are contradicting statements. These statements are having least relevant in the process as they are not pointing to anybody else. Two of them must be TRUE and 2 must be FALSE. There are 4 TRUE and 4 FALSE statements from rest of statements.

We have, 2 FALSE statements among A1, C1, C3 and D2 for sure.

3. Assume A is a car thief. Then only A2, B2 and D3 turns out to be FALSE from rest giving in total of 5 FALSE statements only.

4. Assume C is a car thief. Then only A2, D1 and D3 are FALSE, hence total of 5 FALSE statement among all statements.

5. Assume D is a car thief. Then again only A2, B1 and D3 are FALSE, once again total 5 out of 12 given statements are FALSE in the case.

6. Assume B is a car thief. In this case, B3, C2, D1 and D3 turns out to be FALSE. Hence, total 6 out of 12 given statements are FALSE. 

This is exactly as per fact found in the investigation which suggests that exactly 6 out of 12 statements are FALSE. 

Hence, B must be a car thief. 

Puzzle : The Case of Missing Servant

A king has 100 identical servants, each with a different rank between 1 and 100. At the end of each day, each servant comes into the king's quarters, one-by-one, in a random order, and announces his rank to let the king know that he is done working for the day. 

For example, servant 14 comes in and says "Servant 14, reporting in." 

One day, the king's aide comes in and tells the king that one of the servants is missing, though he isn't sure which one.

Before the other servants begin reporting in for the night, the king asks for a piece of paper to write on to help him figure out which servant is missing. 

Unfortunately, all that's available is a very small piece that can only hold one number at a time. The king is free to erase what he writes and write something new as many times as he likes, but he can only have one number written down at a time. 

The king's memory is bad and he won't be able to remember all the exact numbers as the servants report in, so he must use the paper to help him.

How can he use the paper such that once the final servant has reported in, he'll know exactly which servant is missing?

Mathematical Trick to know the missing servant! 

Solution : The Missing Servant in the Case

What was the case?

When the first servant comes in, the king should write his number on the small piece of paper. For every next servant that reports in, the king should add that servant's number to the current number written on the paper, and then write this new number on the paper while erasing old one.

Addition of numbers from 1 to 100 = 5050.

Hence, 

Missing Servant Number = 5050 -  Addition of ranks of 99 Servants.

So, depending on how far the addition of 99 servants' rank goes to near 5050, the king can easily deduce the rank of missing servant.

For example, if the addition that king has after 99 servants report in is 5000 then the servant having rank = 5050 - 5000 = 50 must be missing. 

 

Puzzle by The Mathemagician

Mavis the 'mathemagician' held ten cards (face down) in her hand - Ace (1) to 10 of Hearts.
She moved the top card to the bottom of the pack, counting '1', and turned up the next card, placing it on the table. It was the Ace.

She counted two more cards to the bottom of the pack, showed the next card - the '2' - and placed it on the table. She moved those counted top 2 cards to bottom.

Counting, 'One, two, three' more to the bottom, she then showed the next card - '3' of Hearts followed by moving those counted top 3 to bottom. 

This continued for four to nine, and the final card was - ta-daah! - the '10' of Hearts.

Question: What was the original order of cards, from the top to bottom?

THIS should be the order!