## March 2015 Logic & Maths Problems

1. John, Paul, George, and Ringo all enter a race, but there is nobody at the finish line to judge the ending. When the judge finally shows up to award the prize for coming in first, these are the statements the four of them make:
John: I was neither first nor last.
Paul: I did not finish last.
George: I won the race!
Ringo: I came in last.
The judge starts to hand George the prize, when Yoko, who was watching the race, says, “Exactly one of these four is lying.”
To whom should the judge grant the prize?

2.
In a group of 200 people, everybody has a candle. To begin with, no candles are lit. One person has a match and lights his candle. With this candle he walks to somebody else and lights a new candle. Then everybody with a burning candle will look for somebody without a burning candle, and if found they will light it. This will continue until all candles are lit. Suppose that from the moment a candle is lit it takes exactly 30 seconds to find a person with a non-burning candle and light that candle. From the moment the first candle is lit, how long does it take before all candles are lit?

3.
A train of 1km in length travelling at 60 km / h enters a 1 km long tunnel at exactly 8:00 pm. At what time will it clear the tunnel?

4. My house has a number.
IF that number is a multiple of 3, the number is from 50 to 59 inclusive.
IF the number is NOT a multiple of four, it lies in the range 60 to 69 inclusive.
IF the number is NOT a multiple of 6, it lies in the range 70 to 79 inclusive.
What is my house number?

5. What is the total number of triangles in this diagram?

6. Leo the Liar lies a lot.
He tells the truth only on one of the days of the week.
The days of the week in order are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, Monday, Tuesday etc.
One day Leo said “I lie on both Mondays and Tuesdays”
The following day, he said “Today is either Thursday, Saturday or Sunday”.
The day after that, he said “I lie on both Wednesdays and Fridays”.
On which day of the week does Leo tell the truth?

7.
The picture shows a device for registering the level of a river. A float in the river rises and falls and is connected to a gear train. The gear on the right hand side causes a pointer to move up or down.
Has it been labelled correctly or incorrectly?

8. State the next number in this sequence: 2,3,5,8,13,21, _ _ _

9. How many animals do I have if all but 3 are dogs, all but 3 are cats, all but 3 are pigs and all but 3 are cows?

10.

SOLUTIONS