Puzzle 53
What is the 20th prime number?
2, 3, 5, 7, ...
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Hint
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ...
Answer
71.
The first twenty prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.
Puzzle 54
A trout's tail weighs eight pounds.
Its head weighs as much as the tail and one-half of the body combined, and the body weighs as much as the head and tail combined.
What does the whole trout weigh?
Puzzle Copyright © Kevin Stone
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Hint
A little bit of algebra might help.
Answer
64 pounds.
The head weighs 24 pounds, the body weighs 32 pounds and the tail weighs 8 pounds.
The trout is made up of the head, body and tail, H, B and T.
We are told that:
T = 8
(1) H = T + B ÷ 2
(2) B = H + T
Placing T into (1) and (2) we get:
(3) H = 8 + B ÷ 2
(4) B = H + 8
Using (4) in (3) we get:
H = 8 + B ÷ 2
(5) H = 8 + (H + 8) ÷ 2
Multiplying (5) by 2 we get:
2H = 16 + H + 8
2H = 24 + H
H = 24
Therefore, by (2):
B = H + T
B = 24 + 8
B = 32
Giving:
H = 24
B = 32
T = 8
And a total of 24 + 32 + 8 = 64 pounds.
Puzzle 55
How many hexagon-type shapes, in total, can you find in this puzzle? Clue: there are more than 45.
Puzzle Copyright © Kevin Stone
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Hint
Look at the different sizes.
Answer
There are 64 hexagon-type shapes in total.
There are 37 single hexagons, 19 hexagons that contain 7 smaller hexagons, 7 hexagons that contain 19 smaller hexagons, and one large hexagon that contains all of the smaller hexagons.
Puzzle 56
Starting with any number on the top row, make your way to the bottom, adding the numbers as you go.
Each time you go to the next row, you can move straight down, or one place to the left or right.
What is the highest total you can make? What is the lowest?
Puzzle Copyright © Kevin Stone
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Hint
The lowest route contains more 2's than the highest route.
Answer
Highest = 24. Lowest = 12.
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