Puzzle 1
My friend's son, Billy, has the same number of brothers as sisters.
His sister, Laura, has twice as many brothers as she has sisters.
How many boys and girls are in the family?
Puzzle Copyright © Kevin Stone
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Hint
A little bit of algebra might help.
Answer
There are four boys and three girls.
If we call the number of boys B, and girls G.
From the first statement (we take one off as Billy is a boy):
B − 1 = G
and similarly:
2 x (G − 1) = B
Substitute G from the first equation into the second equation to give:
2 x ((B − 1) − 1) = B
2 x (B − 1) − 2 = B
2 x B − 2 − 2 = B
2 x B − 4 = B
B = 4
which means that B = 4 and hence G = 3.
Puzzle 2
By changing the third letter of each of the words below, can you make another valid word?
You have to change each word such that the third letters will reveal a ten-letter word when read downwards.
Therefore, what now reads 'krzsaprokd ' will be a real word.
bak e
cur e
maz e
pes t
nea t
rop e
por t
foo d
pok e
sod a
Puzzle Copyright © Kevin Stone
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Hint
The first word is base.
Answer
Strawberry.
bake = bas e
cure = cut e
maze = mar e
pest = pea t
neat = new t
rope = rob e
port = poe t
food = for d
poke = por e
soda = soy a
Puzzle 3
Triathlon - Round 2 – All Logic Puzzles
The final of the BrainBashers triathlon was a close run thing.
The whole tournament was decided on the last two sections, cycling and the road race.
Alex didn't win either section.
The person who won the cycling came third in the road race.
Alex beat Charlie in cycling, but was beaten by Charlie in the road race.
Charlie was last in neither section.
Drew won the road race, but was beaten by Billie in the cycling.
Can you work out who came where in each section?
Puzzle Copyright © Kevin Stone
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Hint
In the road race, where could Charlie have finished?
Answer
Cycling : Billie > Alex > Charlie > Drew
Road race : Drew > Charlie > Billie > Alex
Road Race
In the road race, where could Charlie have finished?
By (4), he wasn't last. By (5), he wasn't first.
By (2), if Charlie was third, then he would have won the cycling, but by (3) Alex beat Charlie in the cycling, so Charlie can't have won the cycling.
So Charlie must have finished in second place.
By (5), Drew was first.
By (1), Alex didn't win the cycling, so by (2) he didn't come third in the road race. Therefore, Alex came last.
Leaving Billie in third place.
Road race : Drew > Charlie > Billie > Alex
Cycling
By (2), Billie won.
By (4), Charlie wasn't last.
By (3), Alex beat Charlie. So Alex finished in second place, with Charlie in third place.
Leaving Drew in last place.
Cycling : Billie > Alex > Charlie > Drew
Puzzle 4
What number is …
… one half of one third of one quarter of 360?
Puzzle Copyright © Kevin Stone
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Hint
Try working backwards.
Answer
15.
Reasoning
One quarter of 360 is 90.
One third of 90 is 30.
One half of 30 is 15.
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