Puzzle 1
Place a horizontal or a vertical line into every blank square.
Each number tells you the total length of the lines connected to that square.
Puzzle Copyright © Johan de Ruiter
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Hint
Start by looking at the 6 and 4 on the top row.
Answer
Puzzle 2
Below is a very special grid, around each shaded number are 8 white squares.
However, each white square should have a number from 1 to 7.
Once filled in, these 8 numbers will sum to the shaded number.
In addition, once completed correctly, no row nor column will contain a duplicate number within a white square.
For example, the top row may be 5 6 4 2 3 1 7, etc.
This is a very difficult puzzle, and many people resort to using a computer to help them, which is a challenge in itself.
Puzzle Copyright © Kevin Stone
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Hint
This puzzle almost certainly requires trial-and-error to solve, and there might be more than one solution.
Answer
There might be more than one correct solution.
Puzzle 3
Can you find three consecutive odd numbers that …
… total 7,644,585 when multiplied together?
Puzzle Copyright © Kevin Stone
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Hint
Try starting with the cube root of the number.
Answer
195 x 197 x 199.
Reasoning
Since we're after three numbers that multiply together, a good place to start is the cube root of 7,644,585, which is roughly 196.99.
Let's try dividing by the closest odd number to 196.99:
7644585 ÷ 197 = 38805
We're now after whole divisors of 38,805, so trying either odd number either side of 197 might work.
Trying either 195 or 199 gives the answer.
Double-Checking
195 x 197 x 199 = 7,644,585
Note
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.
Puzzle 4
A grocer has to place 28,121 carrots into bags, each bag containing the same number of carrots, and using as few bags as possible.
If you think that one big bag will suffice, then feel free to calculate its size!
If we assume that more than one bag is used, how many are required?
Puzzle Copyright © Kevin Stone
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Hint
28,121 isn't a prime number.
Answer
61 bags.
Reasoning
Each bag contains 461 carrots.
How do we find the correct answer? An easy way is to keep dividing 28,121 by the prime numbers in sequence until one works.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61.
