Puzzle 5
In Farmer Donald's hay loft there are a number of ants, mice and chickens.
There are ten times as many ants as there are mice, and there are four times as many mice as there are chickens.
Altogether there are 1,806 feet.
How many chickens are there?
Puzzle Copyright © Kevin Stone
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Hint
Think about the number of legs.
Answer
There are 7 chickens, 28 mice and 280 ants.
Reasoning
For every chicken (2 legs) we have 4 mice (16 legs) and 40 ants (240 legs) = 258 legs.
So we can divide the total number of legs by 258, giving 1,806 ÷ 258 = 7 (chickens).
Puzzle 6
During a recent BrainBashers thinking contest(!), the total number of points scored by the first six players was 103 and every score was above zero.
The first player scored half the points of the second player, who in turn scored 6 points fewer than the third player.
The third player in turn scored two thirds the points of the fourth player.
The fifth player managed to score the same number of points as the difference between the first and fourth player's points.
Finally, the sixth player scored 14 fewer points than the fifth player.
Can you determine how many points the sixth player managed to score?
Puzzle Copyright © Kevin Stone
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Hint
The fourth player is the key to this tricky question.
Answer
9 points.
Respectively the scores were 7, 14, 20, 30, 23, 9.
Reasoning
If we label the six players A, B, C, D, E, and F, we know that:
[1] A + B + C + D + E + F = 103
and from the clues:
A = B ÷ 2
B = C – 6
C = D x 2 ÷ 3
E = D – A
F = E – 14
If instead we choose E = A – D, we'd later see that we end up with a negative value for E, which isn't allowed.
Since D is the letter we're missing information for, it's best to find all of the other letters in terms of D.
These steps are left as an exercise (use C in the equation for B, etc), but the result is:
A = ( D – 9) ÷ 3
B = (2D – 18) ÷ 3
C = (2D ) ÷ 3
D = (3D ) ÷ 3
E = (2D + 9) ÷ 3
F = (2D – 33) ÷ 3
Writing it as D = 3D ÷ 3 makes it slightly clearer to see, when adding in the next step.
We can then use these in [1] to find that 12D = 360, so D = 30.
Therefore, F = 9.
Puzzle 7
Using all of the letters A to Z, each once only, complete these common words.
cl--h
co--h
di-r-
-rea-
in-e-
-ok-r
-a-or
-ua-l
re-e-
-to-e
s-am-
ya--t
-eb-a
Puzzle Copyright © Kevin Stone
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Hint
The 4th word begins with the letter F.
Answers
cl--h = cloth (OT)
co--h = cough (UG)
di-r- = diary (AY)
-rea- = freak (FK)
in-e- = index (DX)
-ok-r = joker (JE)
-a-or = manor (MN)
-ua-l = quail (QI)
re-e- = rebel (BL)
-to-e = stove (SV)
s-am- = swamp (WP)
ya--t = yacht (CH)
-eb-a = zebra (ZR)
This puzzle isn't guaranteed to have a unique answer, can you find another?
Puzzle 8
Two friends were driving from their home to Manchester, Alex drove the first 90 miles, and Billie took over for the remainder of the journey.
On the way back, Alex drove to begin with, and Billie took over for the last 100 miles.
Who drove the furthest?
Puzzle Copyright © Kevin Stone
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Hint
It doesn't matter how far it was to Manchester, so you can use any distance.
Answer
Billie.
Reasoning
If we call the one way distance T, we know that:
On the way there, Alex drove 90 miles, and Billie drove (T – 90) miles.
On the way back, Alex drove (T – 100) miles, and Billie drove 100 miles.
So, in total, both ways:
Alex drove 90 + (T – 100)
= T – 10
Billie drove (T – 90) + 100
= T + 10
Therefore, Billie drove 20 miles more than Alex.
