Puzzle 13
Downhill Mountain Bike Race - Logic Puzzles
At the recent BrainBashers downhill mountain bike race, four entrants entered the challenging slalom event.
Alex finished in first position.
The entrant wearing number #2 wore red, but Drew didn't wear yellow.
The person in last place wore blue, and Stevie wore number #1.
Glen beat Stevie, and the person who finished in second wore number #3.
The entrant in yellow beat the entrant in green.
Only one of the entrants wore the same number as their final position.
Can you determine who finished where, the number, and colour they wore?
Puzzle Copyright © Kevin Stone
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Hint
Start by looking at where Alex finished, and where the person who wore #3 finished, and then use clue (6).
Answer
Pos Name Wore Colour
1 Alex #2 red
2 Glen #3 yellow
3 Stevie #1 green
4 Drew #4 blue
Reasoning
The four colours were: blue, green, red, yellow.
The four contestants were: Alex, Drew, Glen, Stevie.
By (1), Alex was first.
1 Alex
2
3
4
By (4), the person who was second wore number #3.
1 Alex
2 #3
3
4
Looking at (6):
- first place (Alex) can't have worn #1, because, by (3), Stevie wore #1
- second place wore #3
- third place can't have worn #3, because it was worn by second place
- fourth place is the only entrant who could have worn the same number as their final position
Therefore, Stevie finished in third, and Alex wore #2.
1 Alex #2
2 #3
3 Stevie #1
4 #4
By (2), Alex wore red. By (3), the person wearing blue was last.
1 Alex #2 red
2 #3
3 Stevie #1
4 #4 blue
By (5), yellow beat green.
1 Alex #2 red
2 #3 yellow
3 Stevie #1 green
4 #4 blue
By (4), Glen beat Stevie.
1 Alex #2 red
2 Glen #3 yellow
3 Stevie #1 green
4 #4 blue
Leaving Drew in last place.
1 Alex #2 red
2 Glen #3 yellow
3 Stevie #1 green
4 Drew #4 blue
Puzzle 14
Complete these four letter words.
The first letters form a word reading down, and the last letters form a word that is related to the first.
Puzzle Copyright © Kevin Stone
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Hint
The first word starts with H.
Answer
Hard and soft.
H |
A |
T |
S |
A |
L |
S |
O |
R |
O |
O |
F |
D |
E |
B |
T |
Puzzle 15
How many squares, of any size, can you find on this chessboard that do not contain a Rook?
Puzzle Copyright © Kevin Stone
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Hint
How many 2x2 squares are there?
Answer
128.
Reasoning
There are 62 squares of size 1 x 1.
There are 41 squares of size 2 x 2.
There are 18 squares of size 3 x 3.
There are 6 squares of size 4 x 4.
There is 1 square of size 5 x 5.
A total of 62 + 41 + 18 + 6 + 1 = 128.
Puzzle 16
If four kittens can catch four toys in four minutes...
...how many toys can twelve kittens catch in twelve minutes?
Puzzle Copyright © Kevin Stone
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Hint
How many toys can one kitten catch in twelve minutes?
Answer
36 toys.
Reasoning
Four kittens can catch four toys in four minutes,
so
one kitten can catch one toy in four minutes,
so
one kitten can catch three toys in twelve minutes,
so
twelve kittens can catch 36 toys in twelve minutes.
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