Puzzle 5
Billy has twice as many sisters as brothers.
His sister, Frankie, has one more sister than she has brothers.
How many boys and girls are there in the family?
Puzzle Copyright © Kevin Stone
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Hint
The answer isn't very large at all.
Answer
There are four boys and six girls in the family.
If there were B boys, and G girls we know that Billy has twice as many sisters as brothers, so 2 x (b − 1) = g.
And his sister, Frankie, has one more sister than she has brothers, so g − 1 = b + 1.
2(b − 1) = g [1]
g − 1 = b + 1 [2]
Using [1] in [2] gives:
2(b − 1) − 1 = b + 1
Expanding the bracket gives:
2b − 2 − 1 = b + 1
Simplifying the left hand side gives:
2b − 3 = b + 1
Add 3 to each side gives:
2b = b + 4
Subtract b from both sides gives:
b = 4
Using b = 4 in [1] gives:
2(4 − 1) = g
6 = g
Puzzle 6
Using a tap, a container of 9 litres and a container of 4 litres …
… can you measure 6 litres?
Puzzle Copyright © Kevin Stone
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Hint
Fill the 9-litre container first.
Answer
Here are the contents of the containers after each stage:
A = 9 litres, B = 4 litres
A B
9 0 fill A
5 4 fill B from A (leaving 5 litres in A)
5 0 empty B
1 4 fill B from A (leaving 1 litre in A)
1 0 empty B
0 1 fill B from A
9 1 fill A
6 4 fill B from A (only 3 more litres fit in B)
6 0 empty B
This leaves 6 litres in container A.
Puzzle 7
If tomorrow's yesterday is today…
…what day is yesterday's tomorrow?
Puzzle Copyright © Kevin Stone
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Hint
Tomorrow's yesterday is always today.
Answer
Today.
Reasoning
Tomorrow's yesterday is always today.
And yesterday's tomorrow is also always today.
Puzzle 8
Which fruit comes next in this sequence:
banana · pear · kiwi · tomato · ?
Choose from:
peach, lemon, plum, guava
Puzzle Copyright © Kevin Stone
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Hint
Look at the second letter in each word.
Answer
Guava.
The second letter of the words are the vowels (AEIOU) in order.
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