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 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!

Solution of Mathemagician's Puzzle

What was the MAGIC?

Let us name ten cards as C1, C2, C3.....C10 and initially they are in order like below.

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10

1. Mavis the 'mathemagician' 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. 

Therefore, card C2 must be the Ace. C2 = ACE. 

So, the order has to be as -

C1 ACE C3 C4 C5 C6 C7 C8 C9 C10.

She moved top card to the bottom & kept Ace card on the table.

C3 C4 C5 C6 C7 C8 C9 C10 C1 

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

Therefore, the card C5 must be '2'. C5 = 2.

C3 C4 2 C6 C7 C8 C9 C10 C1 

Moved C3, C4 to the bottom while keeping C5 = 2 on the table.

C6 C7 C8 C9 C10 C1 C3 C4

3. Counted 3 more cards to the bottom of the pack, found '3' as next card. So, the card C9 must be '3'. C9 = 3.

C6 C7 C8 3 C10 C1 C3 C4

Moved C6, C7 and C8 to the bottom while keeping C9 = 3 on table.

C10 C1 C3 C4 C6 C7 C8

4. Counted 4 more cards to the bottom of the pack, found '4' as next card. So, the card C6 must be '4'. C6 = 4.

C10 C1 C3 C4 4 C7 C8

Moved C10, C1, C3 and C4 to the bottom while keeping C6 = 4 on table.

C7 C8 C10 C1 C3 C4

5. Counted 5 more cards to the bottom of the pack, found '5' as next card. So, the card C4 must be '5'. C4 = 5.

C7 C8 C10 C1 C3 5

Moved C7, C8, C10, C1, and C3 to the bottom while keeping C4 = 5 on table.

C7 C8 C10 C1 C3

6. Counted 6 more cards to the bottom of the pack where count goes to the top of the pack after 5, found '6' as next card. So, the card C8 must be '6'. C8 = 6.

C7 6 C10 C1 C3 

Moved C7 to the bottom while keeping C8 = 6 on table.

C10 C1 C3 C7

7. Counted 7 more cards to the bottom of the pack where count goes back to the top of the pack after 4, found '7' as next card. So, the card C7 must be '7'. .C7 = 7

C10 C1 C3 7

Moved C10, C1 and C3 to the bottom while keeping C8 = 6 on table. 

C10 C1 C3.

8.  Counted 8 more cards to the bottom of the pack where count goes back to the top of the pack after 3 and 6, found '8' as next card. So, the card C3 must be '8'. .C3 = 8

C10 C1 8

Moved C10, C1 to the bottom of the pack while keeping C3 = 8 on table.

C10 C1 

9. Counted 9 more cards to the bottom of the pack where count goes back to the top of the pack after 2, 4, 6 and 8, found '9' as next card. So, the card C1 must be '9'. .C1 = 9

C10 9. 

Keeping C1 = 9 on the table leaves only 1 card in the deck.

C10

10. The final card was - ta-daah! - the '10' of Hearts. Hence, .C10 = 10

So the initial order of

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10

must be 

9 A 8 5 2 4 7 6 3 10