RIDDLES & PUZZLES - courtesy of Prof. Layton

DIGITAL DIGITS

Imagine a digital clock like the one shown below. How many times will the clock display three of more of the same number in a row over the course of one day?
 
In case you were wondering, the clock in this puzzle displays time on a 12-hour scale, not on military time

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33333

Use each of the numbers one through nine exactly once to fill in the blanks and complete this equation.

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5 SUSPECTS

Five suspects are called into police headquarters for questioning. They give the following statements.
 A: "One of the five of us is lying."
 B: "Two of the five of us are lying."
 C: "I know these guys, and three of the five of us are lying."
 D: "Don't listen to a word they say. Out of the five of us, four are lying."
 E: "All five of us are dirty rotten liars!"
 
The police only want to release the suspects who are telling the truth. How many people should they let go?

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SINKING SHIP

SOS! Fifteen people are trapped aboard a ship that's going to sink in exactly 20 minutes. Their only chance for survival is the five-person life raft stowed on their vessel. To make matters worse, the waters around the ship are teeming with man-eating sharks, so swimming to safety is out of the question.
 
A round-trip to the nearest island and back to the boat takes nine minutes on the raft. How many people will live to see dry land?

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1000 TIMES

What on earth is this message getting at? The following is written on a piece of paper you picked up:
 
"_ is 1000 times _ _ "
 
To turn this strange message into a proper sentence, all you need to do is fill in the _ with a single letter of the alphabet. But what letter could it be?
 
You'll need to use the same letter for all three _ s.

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OTTF

Here you have a set of small paper cards. On each card is a single letter, but one of the cards is missing its letter. What letter belongs on the blank card

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THE ODD SANDWICH

Using scraps left over from your breakfast, you've managed to cobble together a rather oddly shaped sandwich.
 
How many times must you cut the sandwich in order to make it fit neatly in the container?

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BROTHER AND SISTER

A boy and his big sister are sitting around the kitchen table chatting.
 
"You know, Sis, if I took away two years from my age and gave them to you, you'd be twice my age, huh!"
 
"Well, why don't you just give me one more on top of that? Then I'll be three times your age."
 
So just how old is each sibling?