Puzzle 33
What number is …
… three-quarters of eight-ninths of one-half of 2001?
Puzzle Copyright © Kevin Stone
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Hint
Can the fractions be simplified?
Answer
667.
Reasoning
3 8 1
— of — of — of 2001
4 9 2
which simplifies to:
24
—— of 2001
72
which simplifies to:
1
— of 2001
3
Giving 667.
Puzzle 34
How many squares of any size on this chessboard do not contain a rook?
Puzzle Copyright © Kevin Stone
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Hint
How many 2 x 2 squares are there?
Answer
There are 128 squares without a rook.
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.
Giving a total of 62 + 41 + 18 + 6 + 1 = 128 squares.
Puzzle 35
I recently travelled from my home town to a distant music concert, on a pedal tricycle, of all things! My wonderful, three-wheeled tricycle.
I knew that the epic 2,345 mile trip would wreak havoc on the tyres, but luckily I took along 4 spares!
Instead of waiting for any single tyre to fail, I decided that I would rotate the tyres evenly, making sure that by the end of the trip, all seven tyres had travelled exactly the same distance.
What was the distance that each tyre travelled?
Puzzle Copyright © Kevin Stone
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Hint
How many tyre miles were travelled?
Answer
1,005 miles.
Reasoning
A total of 2,345 miles were travelled and at any one time, three tyres were on the tricycle.
Therefore, 3 x 2,345 = 7,035 tyre miles were travelled, which was shared equally by the 7 tyres.
And 7,035 ÷ 7 = 1,005.
Puzzle 36
Can you find a number such that …
… its double is fourteen more than its quarter?
Puzzle Copyright © Kevin Stone
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Hint
The number is less than 20.
Answer
8.
Reasoning
We need a number (N) such that:
2 x N = 14 + N
—
4
Multiply throughout by 4 to give:
8 x N = 56 + N
So:
7 x N = 56
So N = 8.
Double-Checking
Its double is 16.
Its quarter is 2.
So its double is fourteen more than its quarter.
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