Puzzle 7

Hi! At long last, the biweekly puzzles have returned! Apologies as I was too busy last Wednesday... Anyway, if you didn't like last week's puzzle you're going to hate this puzzle. This is not only about logic, but also about maths. (That's right Joyce -- I'm referring to you!) It's LOGICAL MATHEMATICS! Actually most of maths is logical, so maybe it should be mathematical logic? Never mind, here's the puzzle!

LIAR, LIAR (PART 2)

Difficulty: Hard

There are 2 questions to solve in total.

1. 6 mathematicians gathered around a table and discussed about their ages. There is a peculiar condition about this group of mathematicians. Those whose ages are above 40 are truthful unless their age is a multiple of 13. Those whose ages are below 40 are lying unless their age is a multiple of 7. Each of them said:

1. Number 6 is older than me by 11 years. Number 4 is at least 70 years old.
2. Number 4 is 68. I am not 32.
3. I am 44. Number 5 is older than me by 8 years.
4. I am 65.
5. Number 2 is lying. Number 1 is 28.
6. Number 3 is telling the truth.

None of the mathematicians are over 80 years old. Their total age is 273. Find their ages respectively.

2. You are walking home one day from school late at night. There is no one around. Suddenly, someone knocks you out from behind! When you wake up, you find yourself in a dark, musty room. You have been kidnapped! Your parents are on a business trip and won't be back till next week, and tommorow's a Saturday, so no teachers/friends will report you missing.

The windows are barricaded. The door is locked, but it is wired to something. You follow the wires and realise it is connected to... a bomb! The digital clock on it flashes on and starts counting down...

You frantically try to use your phone and call for help, but there's no reception! Carefully, you examine the bomb, to see if it can be deactivated. You find that you are required to input a numerical code. Perhaps that will deactivate the bomb!

On the floor next to the bomb is a sheet of paper, scrawled on it was:

Clues for the code:

1. It has only 2 digits.
2. It is a factor of 192.
3. It is not 192.
4. It is a multiple of 32.

Note to self:
Digits of code when added together is 12.
1 of the clues is wrong!

Quick! Before you get exploded to bits, what is the code?

Now for the answer to Puzzle 6... You know what to do!

1. Phil and David, who just happened to be the 1P's chairperson and vice-chairperson. David was also the outright liar.

2. Statements 2, 4 and 5.

3. Suspect A can't be lying since Suspect E will be lying too. Suspect B can't be lying since Suspect C will be lying too. Suspect D can't be lying since both Suspect D and E will be the shoplifters, and there can only be one.
So who is lying then? Remember the witness? He lied about the 5 suspects, so he's the shoplifter!

4. Bridgette stole the answers. Douglas was the liar.

:)
Glen