Puzzle 17
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 puzzle is easier than it first appears.
Answer
15.
Using normal mathematics!
5/15 of 45 = 1/3 of 45 = 15.
Puzzle 18
Can you highlight exactly three numbers that add to 17?
Note: this puzzle is not interactive, and the numbers cannot be clicked.
Puzzle Copyright © Kevin Stone
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Hint
You have to highlight three numbers.
Answer
2 + 13 + 2 = 17.
The puzzle didn't ask for three digits to be highlighted!
Puzzle 19
After a day picking strawberries, I ended up with a full basket, which is always nice.
I ate 5, and then gave Alex half of the remaining.
I ate another 3, and then 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
Try working backwards.
Answer
335 strawberries.
Reasoning
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.
Double-Checking
I started with 335.
I ate 5, leaving 330.
I gave Alex half (165), leaving 165.
I ate 3, leaving 162.
I gave Billie one third (54), leaving 108.
I ate 6, leaving 102.
I gave Charlie two thirds (68), leaving 34.
Puzzle 20
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.
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