Puzzle 785
In which sport do winners move backwards and losers move forwards?
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Puzzle 786
Can you find three consecutive odd numbers that...
...total 1,287 when multiplied together?
Puzzle Copyright © Kevin Stone
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Hint
Try starting with the cube root of the number.
Answer
9 x 11 x 13.
Reasoning
Since we're after three numbers that multiply together, a good place to start is the cube root of 1,287, which is roughly 10.88.
Let's try dividing by the closest odd number to 10.88:
1287 ÷ 11 = 117
We're now after whole divisors of 117, so trying either odd number either side of 11 might work.
Trying either 9 or 13 gives the answer.
Double-Checking
9 x 11 x 13 = 1,287
Note
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.
Puzzle 787
If I can boil 2 eggs in 10 minutes.
How long will it take me to boil 5 eggs?
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Hint
Be careful with your thinking.
Answer
Exactly the same time!
Puzzle 788
You can imagine an arrow in flight, toward a target. For the arrow to reach the target, the arrow must first travel half of the overall distance from the starting point to the target. Next, the arrow must travel half of the remaining distance.
For example, if the starting distance was 10m, the arrow first travels 5m, then 2.5m.
If you extend this concept further, you can imagine the resulting distances getting smaller and smaller. Will the arrow ever reach the target?
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Hint
This puzzle needs some very careful thinking.
Answer
Yes.
Since the arrow does indeed hit the target, it must be true that 1/2 + 1/4 + 1/8 + ... = 1.
This is because the sum of an infinite series can be a finite number.
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