Puzzle 37
How many squares, of any size, can you find on this chessboard which do not contain a Rook?
Puzzle Copyright © Kevin Stone
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Hint
How many 2x2 squares are there?
Answer
93.
There are 60 squares of size 1x1.
There are 33 squares of size 2x2.
A total of 60 + 33 = 93.
Puzzle 38
If
7/28 of 64 is 16 and
9/12 of 100 is 75 and
3/9 of 33 is 11
what is 5/15 of 45?
Puzzle Copyright © Kevin Stone
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Hint
This is easier than it might first appear.
Answer
15.
Using normal mathematics!
Puzzle 39
After a day picking strawberries I had a basket full.
I ate 5 and gave Alex half of the remaining.
I then ate another 3 and gave Billie one third of the remaining.
I ate another 6 and then gave Charlie two thirds of the remaining.
I now had 34 strawberries left. How many did I start with?
Puzzle Copyright © Kevin Stone
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Hint
What fraction of them did I eat?
Answer
335 strawberries.
Working backwards...
I ended up with 34 strawberries, so I had 102 before giving Charlie two thirds.
I ate 6 myself, so I had 108 before I ate those.
I had 108 strawberries, so I had 162 before giving Billie one third.
I ate 3 myself, so I had 165 before I ate those.
I had 165 strawberries, so I had 330 before giving Alex one half.
Ate 5 myself, so I had 335 before I ate those.
Therefore I started with 335 strawberries.
Puzzle 40
You have a very large number of generic plastic building blocks, each in the shape of a cube.
Think about how many cubes you would need in order to construct a giant cube with 16 small cubes along each edge.
If you were to then remove the outside layer, how many small cubes would you have removed?
Puzzle Copyright © Kevin Stone
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Hint
Think about one face at a time.
Answer
1,352 small cubes.
Reasoning
The original large cube with 16 small cubes along each edge would require 16 x 16 x 16 = 4,096 small cubes.
Removing the outside layer would leave a large cube now with 14 small cubes along each edge (which requires 14 x 14 x 14 = 2,744 small cubes).
It isn't 15 small cubes because you're removing both ends of an edge.
Therefore, you have removed 4,096 - 2,744 = 1,352 small cubes.
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