Puzzle 613
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 614
Can you find every occurrence of the word MARCH that appears in this grid (horizontally, vertically, or diagonally)?
The hint will reveal the number of times it occurs, but where are they?
Note: this puzzle is not interactive, and the letters cannot be selected.
Puzzle Copyright © Kevin Stone
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Hint
The word MARCH appears 46 times.
Answer
The word MARCH appears 46 times.
Puzzle 615
Can you find every occurrence of the word JANUARY that appears in this grid (horizontally, vertically, or diagonally)?
The hint will reveal the number of times it occurs, but where are they?
Note: this puzzle is not interactive, and the letters cannot be selected.
Puzzle Copyright © Kevin Stone
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Hint
The word JANUARY appears 10 times.
Answer
The word JANUARY appears 10 times.
Puzzle 616
Imagine a bottle recycling skip, empty other than one lonely bottle.
Every hour, on the hour, people come and put bottles into the skip.
The first hour, at noon, one person came and put a bottle in.
One hour later, two people each placed a bottle into the skip.
An hour later, four people each placed a bottle into the skip.
This doubling of people continued until 11pm, when the skip was finally full.
When was the skip exactly half full?
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Hint
Remember that the bottle count doubles each time.
Answer
10pm.
Reasoning
The skip started with 1 lonely bottle.
At Noon: 1 person came along and added a bottle, making the total 2 bottles.
At 1pm: 2 people came along and each added a bottle, making the total 2 + 2 = 4 bottles.
At 2pm: 4 people came along and each added a bottle, making the total 4 + 4 = 8 bottles.
At 3pm: 8 people came along and each added a bottle, making the total 8 + 8 = 16 bottles.
Therefore, the number of bottles in the skip is doubling every hour, as it was full at 11pm, it must have been half full at 10pm.
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