## August 2014 Logic & Maths Puzzles

1. Rob, Randy, Rich and Ray had a race together. Rob couldn’t catch up to Randy and Randy couldn’t catch up with Rich. Rich beat Ray and Rob also beat Ray. What order did they finish in?

2.

This diagram represents a firm’s cabinet of pigeon-holes for leaving messages for its six employees, Alan, Bob. Carl, Dave, Ed and Frank.
Alan’s pigeonhole is directly to the right of Carl’s in the row above Ed’s.
Bob’s and Frank’s pigeonhole are not adjacent in any direction – vertically, horizontally or diagonally.
Carl’s and Dave’s pigeonholes are as far from each other as possible.
Carl’s and Bob’s pigeonholes are on different levels.
List the names of the men with the bottom three pigeonholes in order from left to right.

3. Three painters from three different companies were painting a billboard. The men had three different last names: Red, Blue and Green. The three companies they came from had the same names as the workers. As they were painting, they started talking. “It is funny that all of our last names are different from our companies’ names.” said Mr. Red. “Yes, very strange.” replied the man from Blue & Co.
Who worked for which company?

4. Three volumes of an encyclopaedia are stacked on a shelf as shown.
Each volume has pages numbered from 1 to 100.
A bookworm begins eating at page 1 of volume 1 and eats his way straight through to volume 3 page 100, where he stops. Ignoring covers and flyleaves, how many pages has he eaten?

5. Mr Grant and three friends went to dinner.

Alec sat opposite Don
Brian sat opposite Mr Ford
Mr Hill sat on Brian’s right
Charlie sat in position 2
Alec, Mr Evans and Mr Hill are workmates
Who sat in position 1?

6. A man decides to have a day out and get fit at the same time by setting off from home on a bike. He rides toward his intended destination at 9 km per hour. However, during the ride he sustains a puncture which he quickly realises he cannot repair, so he wheels the bike home at 3 km per hour. Given that he was away from home for eight hours, how far in km did he get before he had to return?

7. One day at a school camp, one twelfth of the group spent the afternoon fishing, and four times as many went horseriding. One half went swimming. The remaining six children played tennis. How many children were attending the camp?

8. 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?

9. How many times faster does the second hand of a clock rotate than the hour hand?

10.
Fred, Irene, Colin and Emily are sitting in a row but not in that order. Emily is not next to Fred or Irene. Fred is sitting on Irene’s immediate left as you look at them. Can you correctly work out who is sitting where?

SOLUTIONS