Puzzle 61
How many squares have been placed in the drawing below?
Puzzle Copyright © Kevin Stone
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Hint
There are fewer than 20 squares.
Answer
18 squares.
In the solution below you can see 6 squares in the middle, with another 12 squares around the outside.
Puzzle 62
Can you find a five-digit number that has no zeros, and no digit is repeated, where:
The first digit is a prime number.
The second digit is the fifth digit minus the first digit.
The third digit is twice the first digit.
The fourth digit is the third digit plus three.
The fifth digit is the difference between the first digit and the fourth digit.
Don't forget that 1 isn't prime, the prime numbers start with 2, 3, 5...
Puzzle Copyright © Kevin Stone
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Hint
Start with the possible answers where the first digit is a prime number, and then look at the third digit.
Answer
23,475.
Reasoning
By (1), the first digit is prime:
2----
3----
5----
7----
By (3), the third digit is twice the first digit, so we can eliminate 5---- and 7----:
2-4--
3-6--
By (4), the fourth digit is the third digit plus three:
2-47-
3-69-
By (5) the fifth digit is the difference between the first digit and the fourth digit:
2-475
3-696
We know from the introduction that no digit is repeated, so we can eliminate 3-696. And, by (2) the second digit is the fifth digit minus the first digit:
23475
Puzzle 63
Hidden in the grid below are eight, 7-letter words.
Each word begins with the central R and you can move one letter in any direction to the next letter. All of the other letters are used exactly once each.
What are the words?
| T |
A |
E |
R |
O |
B |
O |
| E |
T |
G |
S |
T |
N |
W |
| R |
N |
E |
E |
A |
I |
E |
| I |
N |
U |
R |
E |
F |
R |
| N |
B |
U |
O |
E |
E |
E |
| B |
S |
E |
A |
E |
V |
E |
| I |
D |
H |
T |
S |
G |
N |
Note: this puzzle isn't interactive, and the letters can't be clicked.
Puzzle Copyright © Kevin Stone
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Hint
One of the words is RUBBISH.
Answers
Rainbow, referee, revenge, roasted, rubbish, running, retreat, restore.
Puzzle 64
Within the BrainBashers school, the science department has three disciplines.
In total, 280 students study chemistry, 254 students study physics, and 280 students study biology.
In total, 97 students study chemistry and physics, 138 students study physics and biology, and 152 students study chemistry and biology.
73 students study all three disciplines.
Can you determine how many students there are in the science department? The answer is not 814.
Puzzle Copyright © Kevin Stone
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Hint
How many students study chemistry and physics, but not biology?
Answer
500 students.
Reasoning
The answer is more easily seen if three intersecting circles are drawn, and the numbers inside each section are worked out.
We know that 73 students study all three disciplines, which allows us to work out the numbers.
97 students study chemistry and physics, so 97 – 73 = 24 study just chemistry and physics.
138 students study physics and biology, so 138 – 73 = 65 study just physics and biology.
152 students study chemistry and biology, so 152 – 73 = 79 study just chemistry and biology.
280 students study chemistry, so 280 – 73 – 24 – 79 = 104 study just chemistry.
254 students study physics, so 254 – 73 – 24 – 65 = 92 study just physics.
280 students study biology, 280 – 73 – 65 – 79 = 63 study just biology.
For a total of: 104 + 92 + 63 + 24 + 65 + 79 + 73 = 500 students.
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