Puzzle 1
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.
Puzzle 2
Can you find a number such that …
… its double is fourteen more than its quarter?
Puzzle Copyright © Kevin Stone
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Hint
The number is less than 20.
Answer
8.
Reasoning
We need a number (N) such that:
2 x N = 14 + N
———
4
Multiply throughout by 4 to give:
8 x N = 56 + N
So:
7 x N = 56
So N = 8.
Double-Checking
Its double is 16.
Its quarter is 2.
So its double is fourteen more than its quarter.
Puzzle 3
Below, 10 countries have been broken into chunks of letters.
The chunks have been moved around, no chunk is used twice, and all of the chunks are used.
Can you determine what the 10 countries are?
ezu itz zil ela bra gi ia
fi pan mba bel and ber zi
nl bo cam ven dia and um
sw bwe mex erl ico ja li
Puzzle Copyright © Kevin Stone
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Hints
The countries begin with the letters: B, M, B, J, C, S, Z, V, F, L.
Answers
bel-gi-um = Belgium
mex-ico = Mexico
bra-zil = Brazil
ja-pan = Japan
cam-bo-dia = Cambodia
sw-itz-erl-and = Switzerland
zi-mba-bwe = Zimbabwe
ven-ezu-ela = Venezuela
fi-nl-and = Finland
li-ber-ia = Liberia
Puzzle 4
I am a nine-letter word (123456789).
From 6523 grows a plant.
I 689, I 689, I 689, it's no joke.
751 rhymes with you.
421 rhymes too!
What am I?
Puzzle Copyright © Kevin Stone
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Hint
Each number in the poem indicates which letter of the answer is being used.
Answer
Wednesday.
Reasoning
Each number in the poem indicates which letter of the answer is being used.
6523 = seed
689 = say
751 = dew
421 = new
Therefore, '751 rhymes with you' is read as 'dew rhymes with you'.
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