## October 2012 Logic & Maths Puzzles

1. Train Puzzle

Train A leaves station X travelling East at a steady 60 km/hr.

At the same time, Train B leaves station Y travelling West at a steady 50 km/hr.

If the stations are 220 km apart:

a. How far will train A have travelled before the two trains meet?

b. How far will train B have travelled before the two trains meet?

c. How long after setting out will the two trains meet?

2. No Bull

A darts player scores 83 with three darts hitting a treble, a double and a single (no bulls). Given that the three numbers that he hits add up to 36 and the difference between the largest and smallest numbers is 16, can you work out how his score was made up?

3. Suzie-Q

Suzie just could not tell the truth while her friend Samantha (the nice one) just could not tell a lie. The one on the left pointed to her friend and announced “She said she is Suzie!”

Who is the lady on the left?

4. Who’s On First?

Zac, Zeke, and Zelmo are the pitcher, catcher, and first baseman of their baseball team, although not necessarily in that order. In the championship game, the pitcher, an only child, scored the fewest home runs. Zelmo, who dates Zac’s sister, scored more than the catcher. What position does each player play?

5. Tug – O – War

Lenny, Lance, Lulu, and Laura enjoy a good game of tug-o-war. Lance can out-pull Lenny and Lulu together. Lance and Lenny together match up evenly against Laura and Lulu, but if Lulu and Lenny switch places, then Laura and Lenny can win easily. Name the four in order of how strong they are.

6. On Oath

A suspect was questioned in a case he was being accused of. He was asked by the court if his statements were true, and he replied…

I guarantee that it is untenable to deny the opposite of the veracity of my affirmations.”

Is the suspect telling the court the truth or is he lying?

7. The Pot of Beans

A pot contains 75 white beans and 150 black ones. Next to the pot is a large pile of black beans.

A somewhat demented cook removes the beans from the pot, one at a time, according to the following strange rule: He removes two beans from the pot at random. If at least one of the beans is black, he places it on the bean-pile and drops the other bean, no matter what colour, back in the pot. If both beans are white, on the other hand, he discards both of them and removes one black bean from the pile and drops it in the pot.

At each turn of this procedure, the pot has one less bean in it. Eventually, just one bean is left in the pot. What colour is it?

8. Train Puzzle 2

A man needs to go through a train tunnel. He starts through the tunnel and when he gets 1/4 the way through the tunnel, he hears the train whistle behind him.

You don’t know how far away the train is from the tunnel.,

You don’t know how fast the train is going.

You don’t know how fast the man can run.

All you know is that:

If the man turns around and runs back the way he came, he will just barely make it out of the tunnel alive before the train hits him.

If the man keeps running through the tunnel, he will also just barely make it out of the tunnel alive before the train hits him.

Assume the man runs at the same speed whether he goes back to the start or continues on through the tunnel. Also assume that he accelerates to his top speed instantaneously. Assume the train misses him by an infinitesimal amount and all those other reasonable assumptions that go along with puzzles like this!

How fast is the train going compared to the man?

9. Movies, Deodorant & Scrabble

IF the following statements are true:

No men who like movies play scrabble.

All men who use a deodorant play scrabble.

Then is this statement True or False?

No men who use a deodorant like movies.

(It doesn’t matter whether you think the statements are actually true or not, just apply the logic.)

10. Who Stole the Cake?

During a recent investigation, five local villains were interviewed to try and identify who stole a cake. Below is a summary of their statements:

Arnold:  It wasn’t Edward;  It was Brian

Brian:   It wasn’t Charlie; It wasn’t Edward

Charlie: It was Edward; It wasn’t Arnold

Derek:   It was Charlie; It was Brian

Edward:  It was Derek; It wasn’t Arnold

It was well known that each suspect told exactly one lie. For two points, can you determine who stole the cake?

SOLUTIONS