Puzzle 25
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
How large would the smaller cube be?
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.
Puzzle 26
How many squares of any size on this chessboard do not contain a rook?
Puzzle Copyright © Kevin Stone
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Hint
There are no larger squares than size 4x4.
Answer
There are 110 squares without a rook.
Reasoning
There are 60 squares of size 1x1.
There are 35 squares of size 2x2.
There are 12 squares of size 3x3.
There are 3 squares of size 4x4.
Giving a total of 60 + 35 + 12 + 3 = 110 squares.
Puzzle 27
Start in the bottom left corner and move either up or right, one square at a time, adding up the numbers. What is the largest total you can make?
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Note: this puzzle is not interactive, and the squares cannot be clicked.
Puzzle Copyright © Kevin Stone
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Hint
The answer is over 35.
Answer
The largest total that can be made is 37.
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Puzzle 28
Which of the four shapes comes next in this sequence:
Puzzle Copyright © Elliott Line
This puzzle appeared in Mensa's EnigmaSig (193.06) and is used with permission.
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Hint
Perhaps looking around the shapes will help.
Answer
C.
Reasoning
The shapes are the spaces between the digits in the numbers 27, 28, 29, and 30, therefore C is the correct answer, as it is the space between the digits in the number 31.
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